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## Tuesday, July 7, 2015

### 7 7 2015 Using R to generate expression values and compare replicates from qPCR

Today I needed to find a quick efficient way to compare replicate Ct values using R. I've been working recently at taking raw fluorescence data from my qPCR runs and independently generating efficiencies and Ct values for analysis. The first thing to note is all the data below was generated on the BioRAD CFX programming. To export it properly, I had to remove the baseline subtraction which is default for the BioRad to produce. After exporting it, the rest of the analysis is done in R so as to cleanly compare data. The script below was written specifically to deal with the default CSV export from the BioRAD CFX program. If a different thermocycler/program is used the read in and manipulation of the CSV will most likely have to be changed to accomodate whatever format is exported.  repcomparison.R
#Load in required packages for functions below
require(qpcR)
require(plyr)
require(ggplot2)
require(splitstackshape)
#Read in raw fluorescence data from 1st Actin replicate
#Remove blank first column entitled "X"
act3$X<-NULL #Rename columns so that qpcR package and appropriately handle the data act3<-rename(act3, c("Cycle" = "Cycles", "A1" = "H_C_1", "A2" = "N_C_1", "A3"= "S_C_1", "A4"="H_T_1", "A5"="N_T_1","A6"="S_T_1", "A7"="NT_C_1","B1" = "H_C_2", "B2" = "N_C_2","B3"= "S_C_2", "B4"="H_T_2", "B5"="N_T_2", "B6"="S_T_2","B7"="NT_C_2", "C1" = "H_C_3", "C2" = "N_C_3","C3"= "S_C_3","C4"="H_T_3", "C5"="N_T_3", "C6"="S_T_3", "C7"="NT_C_3","D1" = "H_C_4", "D2" = "N_C_4","D3"= "S_C_4", "D4"="H_T_4", "D5"="N_T_4", "D6"="S_T_4", "D7"="NT_C_4","E1" = "H_C_5", "E2" = "N_C_5", "E3"= "S_C_5", "E4"="H_T_5", "E5"="N_T_5", "E6"="S_T_5", "F1" = "H_C_6", "F2" = "N_C_6","F3"= "S_C_6", "F4"="H_T_6", "F5"="N_T_6", "F6"="S_T_6","G1" = "H_C_7", "G2" = "N_C_7", "G3"= "S_C_7", "G4"="H_T_7", "G5"="N_T_7", "G6"="S_T_7", "H1" = "H_C_8", "H2" = "N_C_8","H3"= "S_C_8", "H4"="H_T_8", "H5"="N_T_8", "H6"="S_T_8")) #Run data through pcrbatch in qpcR package which analyzes fluorescence and produces efficiency and cycle threshold values act3ct<-pcrbatch(act3, fluo=NULL) ## Making model for H_C_1 (l4) ## => Fitting passed... ## ## Making model for N_C_1 (l4) ## => Fitting passed... ## ## Making model for S_C_1 (l4) ## => Fitting passed... ## ## Making model for H_T_1 (l4) ## => Fitting passed... ## ## Making model for N_T_1 (l4) ## => Fitting passed... ## ## Making model for S_T_1 (l4) ## => Fitting passed... ## ## Making model for NT_C_1 (l4) ## => Fitting passed... ## ## Making model for H_C_2 (l4) ## => Fitting passed... ## ## Making model for N_C_2 (l4) ## => Fitting passed... ## ## Making model for S_C_2 (l4) ## => Fitting passed... ## ## Making model for H_T_2 (l4) ## => Fitting passed... ## ## Making model for N_T_2 (l4) ## => Fitting passed... ## ## Making model for S_T_2 (l4) ## => Fitting passed... ## ## Making model for NT_C_2 (l4) ## => Fitting passed... ## ## Making model for H_C_3 (l4) ## => Fitting passed... ## ## Making model for N_C_3 (l4) ## => Fitting passed... ## ## Making model for S_C_3 (l4) ## => Fitting passed... ## ## Making model for H_T_3 (l4) ## => Fitting passed... ## ## Making model for N_T_3 (l4) ## => Fitting passed... ## ## Making model for S_T_3 (l4) ## => Fitting passed... ## ## Making model for NT_C_3 (l4) ## => Fitting passed... ## ## Making model for H_C_4 (l4) ## => Fitting passed... ## ## Making model for N_C_4 (l4) ## => Fitting passed... ## ## Making model for S_C_4 (l4) ## => Fitting passed... ## ## Making model for H_T_4 (l4) ## => Fitting passed... ## ## Making model for N_T_4 (l4) ## => Fitting passed... ## ## Making model for S_T_4 (l4) ## => Fitting passed... ## ## Making model for NT_C_4 (l4) ## => Fitting passed... ## ## Making model for H_C_5 (l4) ## => Fitting passed... ## ## Making model for N_C_5 (l4) ## => Fitting passed... ## ## Making model for S_C_5 (l4) ## => Fitting passed... ## ## Making model for H_T_5 (l4) ## => Fitting passed... ## ## Making model for N_T_5 (l4) ## => Fitting passed... ## ## Making model for S_T_5 (l4) ## => Fitting passed... ## ## Making model for H_C_6 (l4) ## => Fitting passed... ## ## Making model for N_C_6 (l4) ## => Fitting passed... ## ## Making model for S_C_6 (l4) ## => Fitting passed... ## ## Making model for H_T_6 (l4) ## => Fitting passed... ## ## Making model for N_T_6 (l4) ## => Fitting passed... ## ## Making model for S_T_6 (l4) ## => Fitting passed... ## ## Making model for H_C_7 (l4) ## => Fitting passed... ## ## Making model for N_C_7 (l4) ## => Fitting passed... ## ## Making model for S_C_7 (l4) ## => Fitting passed... ## ## Making model for H_T_7 (l4) ## => Fitting passed... ## ## Making model for N_T_7 (l4) ## => Fitting passed... ## ## Making model for S_T_7 (l4) ## => Fitting passed... ## ## Making model for H_C_8 (l4) ## => Fitting passed... ## ## Making model for N_C_8 (l4) ## => Fitting passed... ## ## Making model for S_C_8 (l4) ## => Fitting passed... ## ## Making model for H_T_8 (l4) ## => Fitting passed... ## ## Making model for N_T_8 (l4) ## => Fitting passed... ## ## Making model for S_T_8 (l4) ## => Fitting passed... ## ## Calculating delta of first/second derivative maxima... ## .........10.........20.........30.........40.........50 ## .. ## Analyzing H_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... #pcrbatch creates a file with each sample as an individual column in the dataframe. The problem with this is #that I want to compare all the Ct (labelled sig.cpD2) and generate expression data for them but these values have to be #in individual columns. To do this I must transpose the data and set the first row as the column names. act3res<-setNames(data.frame(t(act3ct)),act3ct[,1]) #Now I must remove the first row as it is a duplicate and will cause errors with future analysis act3res<-act3res[-1,] #since the sample names are now in the first column the column title is row.names. This makes analys hard based on the ability to call the first column. #to eliminate this issue, I copied the first column into a new column called "Names" act3res$Names<-rownames(act3res)

#Since each sample name contains information such as Population, Treatment, and Sample Number I want to separate out these factors
#into new columns so that I can run future analysis based on population, treatment, or both. Also note the "drop = F" this is so the original names column remains.
act3res2<-cSplit_f(act3res, splitCols=c("Names"), sep="_", drop = F)

#After splitting the names column into three new columns I need to rename them appropriately.
act3res2<-rename(act3res2, c("Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))

#I also create a column with the target gene name. This isn't used in this analysis but will be helpful for future work.
act3res2$Gene<-rep("Actin", length(act3res2)) #In transposing the data frame, the column entries became factors which cannot be used for equations. #to fix this, I set the entries for sig.eff (efficiency) and sig.cpD2 (Ct value) to numeric. Be aware, without the as.character function the factors will be transformed inappropriately. act3res2$sig.eff<-as.numeric(as.character(act3res2$sig.eff)) act3res2$sig.cpD2<-as.numeric(as.character(act3res2sig.cpD2)) #Now I plot the Ct values to see how they align without converting them to expression. ggplot(act3res2, aes(x=Names,y=sig.cpD2, fill=Pop))+geom_bar(stat="identity") #Now I want to get expression information from my data set. qpcR has a way of doing this but its complicated and I'm not comfortable using it. #Luckily there is an equation I can use to do it. The equation is expression = 1/(1+efficiency)^Ctvalue. I tried multiple ways to get this to work in R #but it doesn't handle the complicated equation easily. #To work around this, I created a function in R to run the equation and produce an outcome. x = efficiency argument, y=Ctvalue argument expr<-function(x,y){ newVar<-(1+x)^y 1/newVar } #Now I run the data through the function and produce a useful expression value act3res2expression<-expr(act3res2$sig.eff, act3res2$sig.cpD2)

#Graphing the expression values is a good way to examine the data quickly for errors that might have occurred.
ggplot(act3res2, aes(x=Names,y=expression, fill=Pop))+geom_bar(stat="identity")

#Before I'm able to compare the replicates I need to process the raw fluorescence from the second Actin run.
#To do this I perform all the same steps as the previous replicate.
act4$X<-NULL act4<-rename(act4, c("Cycle" = "Cycles", "A1" = "H_C_1", "A2" = "N_C_1", "A3"= "S_C_1", "A4"="H_T_1", "A5"="N_T_1","A6"="S_T_1", "A7"="NT_C_1","B1" = "H_C_2", "B2" = "N_C_2","B3"= "S_C_2", "B4"="H_T_2", "B5"="N_T_2", "B6"="S_T_2","B7"="NT_C_2", "C1" = "H_C_3", "C2" = "N_C_3","C3"= "S_C_3","C4"="H_T_3", "C5"="N_T_3", "C6"="S_T_3", "C7"="NT_C_3","D1" = "H_C_4", "D2" = "N_C_4","D3"= "S_C_4", "D4"="H_T_4", "D5"="N_T_4", "D6"="S_T_4", "D7"="NT_C_4","E1" = "H_C_5", "E2" = "N_C_5", "E3"= "S_C_5", "E4"="H_T_5", "E5"="N_T_5", "E6"="S_T_5", "F1" = "H_C_6", "F2" = "N_C_6","F3"= "S_C_6", "F4"="H_T_6", "F5"="N_T_6", "F6"="S_T_6","G1" = "H_C_7", "G2" = "N_C_7", "G3"= "S_C_7", "G4"="H_T_7", "G5"="N_T_7", "G6"="S_T_7", "H1" = "H_C_8", "H2" = "N_C_8","H3"= "S_C_8", "H4"="H_T_8", "H5"="N_T_8", "H6"="S_T_8")) act4ct<-pcrbatch(act4, fluo=NULL) ## Making model for H_C_1 (l4) ## => Fitting passed... ## ## Making model for N_C_1 (l4) ## => Fitting passed... ## ## Making model for S_C_1 (l4) ## => Fitting passed... ## ## Making model for H_T_1 (l4) ## => Fitting passed... ## ## Making model for N_T_1 (l4) ## => Fitting passed... ## ## Making model for S_T_1 (l4) ## => Fitting passed... ## ## Making model for NT_C_1 (l4) ## => Fitting passed... ## ## Making model for H_C_2 (l4) ## => Fitting passed... ## ## Making model for N_C_2 (l4) ## => Fitting passed... ## ## Making model for S_C_2 (l4) ## => Fitting passed... ## ## Making model for H_T_2 (l4) ## => Fitting passed... ## ## Making model for N_T_2 (l4) ## => Fitting passed... ## ## Making model for S_T_2 (l4) ## => Fitting passed... ## ## Making model for NT_C_2 (l4) ## => Fitting failed. Tagging name of NT_C_2... ## ## Making model for H_C_3 (l4) ## => Fitting passed... ## ## Making model for N_C_3 (l4) ## => Fitting passed... ## ## Making model for S_C_3 (l4) ## => Fitting passed... ## ## Making model for H_T_3 (l4) ## => Fitting passed... ## ## Making model for N_T_3 (l4) ## => Fitting passed... ## ## Making model for S_T_3 (l4) ## => Fitting passed... ## ## Making model for NT_C_3 (l4) ## => Fitting failed. Tagging name of NT_C_3... ## ## Making model for H_C_4 (l4) ## => Fitting passed... ## ## Making model for N_C_4 (l4) ## => Fitting passed... ## ## Making model for S_C_4 (l4) ## => Fitting passed... ## ## Making model for H_T_4 (l4) ## => Fitting passed... ## ## Making model for N_T_4 (l4) ## => Fitting passed... ## ## Making model for S_T_4 (l4) ## => Fitting passed... ## ## Making model for NT_C_4 (l4) ## => Fitting failed. Tagging name of NT_C_4... ## ## Making model for H_C_5 (l4) ## => Fitting passed... ## ## Making model for N_C_5 (l4) ## => Fitting passed... ## ## Making model for S_C_5 (l4) ## => Fitting passed... ## ## Making model for H_T_5 (l4) ## => Fitting passed... ## ## Making model for N_T_5 (l4) ## => Fitting passed... ## ## Making model for S_T_5 (l4) ## => Fitting passed... ## ## Making model for H_C_6 (l4) ## => Fitting passed... ## ## Making model for N_C_6 (l4) ## => Fitting passed... ## ## Making model for S_C_6 (l4) ## => Fitting passed... ## ## Making model for H_T_6 (l4) ## => Fitting passed... ## ## Making model for N_T_6 (l4) ## => Fitting passed... ## ## Making model for S_T_6 (l4) ## => Fitting passed... ## ## Making model for H_C_7 (l4) ## => Fitting passed... ## ## Making model for N_C_7 (l4) ## => Fitting passed... ## ## Making model for S_C_7 (l4) ## => Fitting passed... ## ## Making model for H_T_7 (l4) ## => Fitting passed... ## ## Making model for N_T_7 (l4) ## => Fitting passed... ## ## Making model for S_T_7 (l4) ## => Fitting passed... ## ## Making model for H_C_8 (l4) ## => Fitting passed... ## ## Making model for N_C_8 (l4) ## => Fitting passed... ## ## Making model for S_C_8 (l4) ## => Fitting passed... ## ## Making model for H_T_8 (l4) ## => Fitting passed... ## ## Making model for N_T_8 (l4) ## => Fitting passed... ## ## Making model for S_T_8 (l4) ## => Fitting passed... ## ## Calculating delta of first/second derivative maxima... ## .........10.........20.........30.........40.........50 ## .. ## Analyzing H_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing NT_C_1 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_2 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing *NT_C_2* ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_3 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing *NT_C_3* ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_4 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing *NT_C_4* ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_5 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_6 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_7 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_C_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing H_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing N_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... ## ## Analyzing S_T_8 ... ## Calculating 'eff' and 'ct' from sigmoidal model... ## Using window-of-linearity... ## Fitting exponential model... ## Using linear regression of efficiency (LRE)... act4res<-setNames(data.frame(t(act4ct)),act4ct[,1]) act4res<-act4res[-1,] act4res$Names<-rownames(act4res)

act4res2<-cSplit_f(act4res, splitCols=c("Names"), sep="_", drop = F)

act4res2<-rename(act4res2, c("Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))

act4res2$Gene<-rep("Actin", length(act4res2)) act4res2$sig.eff<-as.numeric(as.character(act4res2$sig.eff)) act4res2$sig.cpD2<-as.numeric(as.character(act4res2$sig.cpD2)) ggplot(act4res2, aes(x=Names,y=sig.cpD2, fill=Pop))+geom_bar(stat="identity") expr<-function(x,y){ newVar<-(1+x)^y 1/newVar } act4res2$expression<-expr(act4res2$sig.eff, act4res2$sig.cpD2)

ggplot(act4res2, aes(x=Names,y=expression, fill=Pop))+geom_bar(stat="identity")

#Now that I have Ct values, efficiencies and expression values for both replicates I can create a table of the differences between reps.
#To do this I create a data frame with a single formula that creates a column of values generated by subtracting the first run from the second.
repcomp<-as.data.frame(act3res2$sig.cpD2-act4res2$sig.cpD2)

#Now I need to add some Names for the samples to use with ggplot.Since the names column contains all the relevant information
#I copy only that column and run the split function on it again as well as the rename function.
repcomp$Names<-act3res2$Names
repcomp<-cSplit_f(repcomp, splitCols=c("Names"), sep="_", drop = F)

#To better address the difference column in ggplot I need to rename it something simple and short.
repcomp<-rename(repcomp, c("act3res2$sig.cpD2 - act4res2$sig.cpD2"="rep.diff", "Names_1"="Pop", "Names_2"="Treat", "Names_3"="Sample"))

#Now I just run the data through ggplot to generate a bar graph exploring the differences between the two replicate in terms of Ct values.
ggplot(repcomp, aes(x=Names, y=rep.diff, fill=Pop))+geom_bar(stat="identity")

The results are a little discouraging as the replicates show a maximum a 4 Ct difference which is greater than a 10 fold difference in expression values. I'm running another set of replicates today but have slightly changed the protocol again to hopefully optimize it for tight replicate values.


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# Derivation kalkulator

### Derivative Calculator - Symbola

• derivative\:of\:f(x)=3-4x^2,\:\:x=5; implicit\:derivative\:\frac{dy}{dx},\:(x-y)^2=x+y-1 \frac{\partial}{\partial y\partial x}(\sin (x^2y^2)) \frac{\partial }{\partial x}(\sin (x^2y^2)
• Derivative Calculator Step 1: Enter the function you want to find the derivative of in the editor. The Derivative Calculator supports solving first, second...., fourth derivatives, as well as implicit differentiation and finding the zeros/roots
• Online Derivative Calculator. Enter a valid algebraic expression to find the derivative. Not sure what that means? Type your expression (like the one shown by default below) and then click the blue arrow to submit. Choose Find the Derivative from the menu and click to see the result
• Derivative Calculator with Steps. Enter the function. Use x as your variable. See Examples. f (x) =. . e.g. 2x2 + 3x − 1 x.
• Free Online Derivative Calculator allows you to solve first order and higher order derivatives, providing information you need to understand derivative concepts. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels
• The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc.), with steps shown. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions
• An absolutely free step-by-step first derivative solver

### Derivative Calculator - Mathwa

1. In calculus, the bunda rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let f(x)=g(x)/h(x), where both g and h are differentiable and h(x)≠0. The quotient rule states that the derivative of f(x) is fʼ(x)=(gʼ(x)h(x)-g(x)hʼ(x))/[h(x)]²
2. Free partial derivative calculator - partial differentiation solver step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy
3. Derivative calculator is able to calculate online all common derivatives : sin, cos, tan, ln, exp, sh, th, sqrt (square root) and many more... Thus, to obtain the derivative of the cosine function with respect to the variable x, you must enter derivative_calculator (cos(x); x), result - sin(x) is returned after calculation

### Derivative Calculator - Free Math Hel

1. The derivative calculator allows you to solve any mathematical functions. A simple and easy-to-use interface will be available for you to make the most accurate calculation and study a detailed step-by-step solution of the problem. This derivative calculator is free and can be used from any device
2. An online derivative calculator that differentiates a given function with respect to a given variable by using analytical differentiation. A useful mathematical differentiation calculator to simplify the functions. Enter a function to differentiate (Eg : x^4 + 90*x) Rules for Specifying Input Functio
3. Derivative Calculator The derivative calculator gives chance testing the solutions to calculus exercises. It shows the full working process. The Derivative Calculator helps calculating first, second, fifth derivatives as well as differentiating functions with many variables, implicit differentiation and counting roots, and zeros
4. imum and maximum, of the given function. The calculator will try to simplify result as much as possible. There are examples of valid and invalid expressions at the bottom of the page..
5. Derivative Calculator: Online derivative calculator to find the derivative or partial derivative of a function with respect to a variable
6. The derivative calculator is a free online tool that displays the derivative of the given function. BYJU'S online derivative calculator tool makes the calculations faster, and it shows the first, second, third-order derivatives of the function in a fraction of seconds

### Derivative Calculator with Steps - Open Omni

1. Our online Derivative Calculator gives you instant math solutions with easy to understand step-by-step explanations
2. This calculator calculates the derivative of a function and then simplifies it. The calculator will help to differentiate any function - from simple to the most complex. The program not only calculates the answer, it produces a step-by-step solution. The differentiation order is selected
3. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima
4. This online calculator implements Newton's method (also known as the Newton-Raphson method) using derivative calculator to obtain analytical form of derivative of given function, because this method requires it. Some theory to recall the method basics can be found below the calculator

Our Derivative Calculator tool supports all the most recent functions, computing and several other variables which are essential in 1 tool. Using Math Calculator you'll be in a position to find maximum and minimum simply by clicking a few buttons. Setting the ideal Endpoint Next you ought to see a prompt for the perfect endpoint Solve derivatives using this free online calculator. The deriver function of the calculator makes it possible to compute function derivations online by using the properties of the derivative on the one hand and the derivatives of the usual functions on the other hand Derivative calculator is an equation simplifier which uses derivative quotient rule & derivative formula to find derivative of trig functions. Partial Derivative calculator makes it easy to learn & solve equations

### Derivative Calculator: WolframAlph

Definition of Derivative Calculator online with solution and steps. Detailed step by step solutions to your Definition of Derivative problems online with our math solver and calculator. Solved exercises of Definition of Derivative Derivative Calculator computes derivatives of a function with respect to given variable using analytical differentiation and displays a step-by-step solution. It allows to draw graphs of the function and its derivatives. Calculator supports derivatives up to 10th order as well as complex functions

The derivative calculator is an online tool that gives the derivative of the function. The online derivative calculator tool carries out the computations quicker, and it offers the first, second, third-order derivatives of the operation soon Calculadora gratuita de derivadas - Solucionador de derivadas paso por pas This is our derivative calculator. You can use our tool below to differentiate any continuous function. To use this, simply enter your function and tell us what variable to differentiate on. Please use the following syntax to ensure that we can properly parse your function. For exponents, please use the ^ symbol. For example: x^2 is x to the. This derivative calculator takes account of the parentheses of a function so you can make use of it. E.g: sin(x). This tool interprets ln as the natural logarithm (e.g: ln(x) ) and log as the base 10 logarithm. For instance log 10 (x)=log(x). 15 Apr, 201 Derivative Calculator Online. When solving higher mathematics, it is often necessary to calculate the derivative of a mathematical function. For simple math functions, this is no longer a problem, as tables are developed and accessible for derivatives. However, if you want to find a derivative of a complex mathematical function, you have to.

Free differentiation calculator - Calculate derivations step by step. What is the derivation? The derivation of a function at x says what slope the graph of the function has at x, i.e. what slope a tangent line in the point (x|f(x)) has This calculator finds derivative of entered function and tries to simplify the formula. Use Function field to enter mathematical expression with x variable. You can use operations like addition +, subtraction -, division /, multiplication *, power ^, and common mathematical functions.Full syntax description can be found below the calculator Derivative calculator - step by step . The concept of Derivative is at the core of Calculus and modern mathematics. The definition of the derivative can be approached in two different ways. One is geometrical (as a slope of a curve) and the other one is physical (as a rate of change). We can calculate it for you

Partial Derivative Calculator. In terms of Mathematics, the partial derivative of a function or variable is the opposite of its derivative if the constant is opposite to the total derivative.Partial derivate are usually used in Mathematical geometry and vector calculus.. We are providing our FAM with a lot of calculator tools which can help you find the solution of different mathematical of. Implicit Differentiation Calculator is a free online tool that displays the derivative of the given function with respect to the variable. BYJU'S online Implicit differentiation calculator tool makes the calculations faster, and a derivative of the implicit function is displayed in a fraction of seconds Enter the variable you want the derivative to be calculated with respect to. Enter the the degree of differentiation. The calculator will provide the n'th derivative of the function with respect to the variable. Operators: + (Addition), - (Subtraction), * (Multiplication), / (Division), ^ (Power), ! (Factorial) This online calculator will find the indefinite integral (antiderivative) of the given function, with steps shown (if possible). Show Instructions. In general, you can skip the multiplication sign, so 5x is equivalent to 5*x Derivative calculator quickly solves 1st, 2nd, 3rd and on Derivative equations with graphs and charts. Math Solver is dedicated to help students solve maths equation in simple manner and teach them how solve math problems step-by-step. Our goal is to cover as many equation solver apps and calculators to raise awareness among students

Derivative Calculator SMW 17.12.20 download - The SMW Derivative Calculator does not enforce any derivative order or formula size limits. No interne Derivative Calculator Online derivative calculator finds the derivative of a function with step by step explanations.Please type exp to enter exponential function. Start by entering your function in the input box below. Example: x^(exp(x))+sin(2x), tan(6x)+x/(sin(x)+cos(x)),ln(6x)+arcsin(x+x^2),ln(ln(x+cos(6+x)))+x/tan(x). The above online Product rule derivatives calculator computes a derivative of a given function with respect to a variable x using analytical differentiation. The rule is applied to the functions that are expressed as the product of two other functions. Product Rule of Derivatives: In calculus, the product rule in differentiation is a method of finding the derivative of a function that is the. We write dx instead of Δx heads towards 0.. And the derivative of is commonly written :. x 2 = 2x The derivative of x 2 equals 2x or simply d dx of x 2 equals 2x. What does x 2 = 2x mean?. It means that, for the function x 2, the slope or rate of change at any point is 2x.. So when x=2 the slope is 2x = 4, as shown here:. Or when x=5 the slope is 2x = 10, and so on

Calculus Calculators. Calculus calculators homepage. Below, there is a list of calculus calculators covering issues like derivatives, integrals or limits.. Calculus Calculators. Derivative Calculator. Integral Calculator. Limit Calculato Implicit derivative online calculator Implicit called the function y (x), given by equation: F (x, y (x)) = 0. As a rule, instead of the equation F (x, y (x)) = 0 use notation F (x, y) = 0 assuming, that y is the function of x. As an example of the implicitly defined function, one can point out the circle equation:. Derivative calculator software is designed to solve complex, linear or nonlinear, differential equations. Solving differential equations can be a very time-consuming process, especially if the equation is nonlinear. This software helps you to get to the solution very fast and save time. Some derivative calculator software also has provisions. How to use the Partial Derivative Calculator. Type in a function to solve To get started, enter a value of the function and click «Submit» button. In a moment you will receive the calculation result. See a step-by-step solutio

Derivative of a function is the limit of the infinitesimal change in the function with respect to infinitesimal change in the variable, provided that the last tends to zero: . To find derivative of some function you'd apply basic differentiation rules or use our online step by step derivative calculator.. It capable to calculate second, third and other higher order derivatives The above calculator is an online tool which shows output for the given input. This calculator, makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus.For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes. Latin Wordstock - Latin Vocabulary and Derivatives © 1999-Sumair Mirza and Jason Tsang.All Rights Reserve

To improve this 'Euler's method(2nd-derivative) Calculator', please fill in questionnaire. Male or Female ? Male Female Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school studen Second Derivative Test. Suppose is a function of that is twice differentiable at a stationary point. 1. If , then has a local minimum at . 2. If , then has a local maximum at . The extremum test gives slightly more general conditions under which a function with is a maximum or minimum

### Online Derivative Calculator with Steps - eMathHel

Calculate the Anti-derivative of an Expression. Our free anti-derivative calculator is provided by Mathway and will give the antiderivative of any expression. For full step-by-step work, you'll need to upgrade to their premium membership. Tips. Type the expression for which you want the antiderivative Free math problem solver answers your algebra homework questions with step-by-step explanations The partial derivative calculator on this page computes the partial derivative of your inputted function symbolically with a computer algebra system, all behind the scenes. The computer algebra system is very powerful software that can logically digest an equation and apply every existing derivative rule to it in order You look like the type of person who needs a calculator to do math in their head. — Boyd's Backyard™ (@TheBoydP) January 26, 2019 You look like the type of person who needs a calculator to do math in their head. — Boyd's Backyard™ (@TheBoydP) January 26, 2019 I felt so accomplished by bringing my Continue reading Total Derivative. There are at least two meanings of the term total derivative in mathematics. The first is as an alternate term for the convective derivative.. The total derivative is the derivative with respect to of the function that depends on the variable not only directly but also via the intermediate variables .It can be calculated using the formul

### Free Step-by-Step First Derivative Calculator(Solver

Summary : The sh function allows to calculate online the hyperbolic sine of a number. sh online. Description : Hyperbolic sine function. The calculator allows you to use most hyperbolic functions, it is possible to calculate the hyperbolic cosine (noted ch or cosh), the hyperbolic sine (noted sh or sinh), the hyperbolic tangent (noted th or tanh), and the hyperbolic cotangent (noted coth or. Using a calculator, you will be able to solve differential equations of any complexity and types: homogeneous and non-homogeneous, linear or non-linear, first-order or second-and higher-order equations with separable and non-separable variables, etc. The solution diffusion. equation is given in closed form, has a detailed description

### Calculus Calculator Microsoft Math Solve

Derivative Calculator. 8 896 To se mi líbí · Mluví o tom (9). Online computation of derivatives with steps at www.derivative-calculator.net Derivation in general and vascular surgery patients undergoing inpatient surgery was completed using serial multiple logistic regression. Validation was performed within multiple surgical specialties. Results: The derivation cohort included 88,068 patients, of whom 11,771 (13.4%) were not discharged home. The derived Home Calculator had. This is part of series of videos developed by Mathematics faculty at the North Carolina School of Science and Mathematics. This video demonstrates how to fin.. Integral Calculator The integral calculator allows you to solve any integral problems such as indefinite, definite and multiple integrals with all the steps. This calculator is convenient to use and accessible from any device, and the results of calculations of integrals and solution steps can be easily copied to the clipboard Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube

Online Derivative Calculator (Symbolic Differentiation) Symbolic Derivative Calculator is online tool to find derivative of a given function f(x) with respect to x.Derivative is always with respect to x here! View all Online Tool Download Step-by-Step Derivative Calculator for Windows to compute symbolic derivatives step-by-step and get explanations for each step derivative-calculator. live app: derivative-calculator. Calculates the symbolic derivative of the given function. It parses the expression first using recursive descent parsing and then recusrsively calculates the derivative. It uses MathJax to render mathematical expressions written in AsciiMat This calculator can take the partial derivative of regular functions, as well as trigonometric functions. This user simply enters in the function and the variable to differentiate with respect to. The resultant partial derivative will then be automatically computed and displayed

Calculus: Tangent Line & Derivative. Log InorSign Up. You can edit the equation below of f(x). 1. f x = sin x +. 3 x. 2. You can edit the value of a below, move the slider or point on the graph or press play to animate 3. a = − 5. 8. 4. a, f a. 5. The derivative of f(x) is f '(x) which is g(x). Wipe Save: Warning: This cannot be undone! Toggle Chart: Toggle chart off to increase speed of game. Save: Last save time: None Export Save: Copy this text: Import Sav

### Partial Derivative Calculator - Symbola

Finding the derivative of functions is crucial to solving many different types of math problems. Many electronics problems utilize differentiation to solve for unknowns, including many electromagnetics problems. Related Resources. Capacitor Impedance Calculator Capacitive Reactance How to Calculate the Current Through a Capacito #include stdafx.h // Header file usually use in MS-VS #include <iostream> // Input / Output stream header file some IDE use <iostream.h> #include <conio.h> // for basic console operation using namespace std; /* Namespaces are like drawers in a filing cabinet. All of the standard library is in one drawer, and the only way to get to the stuff in that drawer is to tell C++ where to find it FunctionalCalculator is a simple Java based application that can be used as a derivative calculator. Just enter the function and click Enter, after which the derivative of the function is calculated. It can also be used as an integral calculator, tangent calculator, GCD calculator, and to solve system of linear equations partial-derivative-calculator. ar. image/svg+xml. Related Symbolab blog posts. High School Math Solutions - Derivative Calculator, Products & Quotients . In the previous post we covered the basic derivative rules (click here to see previous post). We are now going.. Derivative Calculator • With Steps! Above, enter the function to derive. Differentiation variable and more can be changed in Options. Click Go! to start the derivative calculation. The result will be shown further below. How the Derivative Calculator Works For those with a technical back. www.derivative-calculator.ne

Learn how to use the derivative calculator with a step-by-step procedure. Get the derivative calculator available online for free only at CoolGyan Notations used in Partial Derivative Calculator. Let f be a function in x,y and z. First order partial derivatives are represented by $\dfrac{\partial f}{\partial x} = f_x$ Second order partial derivatives given by $\dfrac{\partial^2 f}{\partial x^2} = f_{xx}$ The mix derivative is shown by \$ \dfrac{\partial^2 f}{\partial x^2} = f_{xx. Derivative Engines offers two type of products for the small investors. One is Limited Currency Option Calculator, second is the UnLimited Currency Option Pricing Tool.Users who registered to Derivative Engines with their email which is also used in their Linked In account will have free access guarantee to UnLimited Currency Option Pricing Tool untill the end of 2018 for a limited time Partial Derivative Calculator A step by step partial derivatives calculator for functions in two variables. You may first want to review the rules of differentiation of functions and the formulas for derivatives The derivative of a function f(x) is written f'(x) and describes the rate of change of f(x). It is equal to slope of the line connecting (x,f(x)) and (x+h,f(x+h)) as h approaches 0. Evaluating f'(x) at x_0 gives the slope of the line tangent to f(x) at x_0

This program allows you to find the symbolic derivative of any function on the TI-84 Plus CE graphing calculator. How Does it Work? All you have to do is type the function you would like to find the derivative of in Y1. Then, just run the program, and it will store the symbolic derivative in Y2. Requirements >> TI-84 Plus CE Calculato This is the original method in finding the derivative of any equations using the Increment Method. If you know already the List of Formulas to find a derivative of a certain equation, then you can use it. If you don't remember the formulas, then you have to use the Increment Method and it is a long process to do it Derivative Calculator was added by MediaTools in Jun 2020 and the latest update was made in Jun 2020. The list of alternatives was updated Oct 2020. It's possible to update the information on Derivative Calculator or report it as discontinued, duplicated or spam Super-duper online matrix derivative calculator vs. the matrix normal (for Stan) Posted by Bob Carpenter on 3 June 2020, 3:00 pm I'm implementing the matrix normal distribution for Stan, which provides a multivariate density for a matrix with covariance factored into row and column covariances

### Derivative calculator - Online differentiation - Solumath

The Calculator can find derivatives using the sum rule, the elementary power rule, the generalized power rule, the reciprocal rule (inverse function rule), the product rule, the chain rule and logarithmic derivatives. Of course trigonometric, hyperbolic and exponential functions are also supported. Integrals / Antiderivative Type in a mathematical function and get the derivative, and the nth derivative. You can also plug values into the functions and get their output Derivative by first principle refers to using algebra to find a general expression for the slope of a curve. It is also known as the delta method. The derivative is a measure of the instantaneous rate of change, which is equal to. Partial Derivative Calculator: Are you scared of finding the partial derivatives? To help you in this we have given the free Partial Derivative Calculator that does all your derivative calculations in fraction of seconds. We have included the step by step procedure on how to solve the partial differential equation The following problems require the use of the limit definition of a derivative, which is given by They range in difficulty from easy to somewhat challenging. If you are going to try these problems before looking at the solutions, you can avoid common mistakes by making proper use of functional notation and careful use of basic algebra

The derivative of the natural logarithmic function (ln[x]) is simply 1 divided by x. This derivative can be found using both the definition of the derivative and a calculator. Derivatives of logarithmic functions are simpler than they would seem to be, even though the functions themselves come from an important limit in Calculus Second Order Partial Derivative Calculator. Enter Function: Differentiate with respect to:. Complex Number&Matrix Calculator | Graphing&Derivative Calculator. You can use any of the calculators below or use the MathCalc all-in-one calculator which comprises all the below calculators for graphing, complex matrix algebra and complex number calculations, and differentiation.. Complex Matrix Calculator Calculate complex matrix expressions and perform matrix operations involving complex. Find a Derivative Using the Quotient Rule. The quotient rule is a formula for finding the derivative of a fraction. This page will show you how to take the derivative using the quotient rule. Type the numerator and denominator of your problem into the boxes, then click the button

Integral Calculator computes an indefinite integral (anti-derivative) of a function with respect to a given variable using analytical integration. It also allows to draw graphs of the function and its integral. Please remember that the computed indefinite integral belongs to a class of functions F(x)+C, where C is an arbitrary constant Derivative calculator computes derivative of a function using symbolical differentiation and displays a step-by-step solution This is the Facebook page for the Derivative Calculator. Try it here: https://www.derivative-calculator.net

### Derivative Calculator with Steps - 100% Fre

The SMW Derivative Calculator does not enforce any derivative order or formula size limits. No internet connection is required by entering the desired formula in the infix format and calculate. Characteristics: * Create formulas quickly with our custom keyboard; * Compute the derivative of any function, including trigonometric (and inverse), logarithmic and neperian functions; * Activate or. Partial Derivative Calculator. Author: mpodman. Topic: Derivativ

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# How do you convert 255 degrees to radians?

Jan 14, 2016

#### Explanation:

Using the relationship that exists between degrees and radians

ie${180}^{\circ} = \pi$ radians

then ${255}^{\circ} = \frac{\pi}{180} \times 255 = 4.45$


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# User Portlet

David Arnold
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At school, I am teaching on a Windows 7 using Mathematica 10.2.0 (soon to be updated to 10.3.1.0). I am using SmartBoard version 14.2.953.0. I cannot get the SmartBoard pen to draw on top of the Mathematica notebook. Is there a workaround for...
The creation of the pdf failed. I can report that the changing to bitmap worked. We were able to print, although the image sizes were larger than in the notebook. Our technology support has a lot to work on, as I can print the file from my office...
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# Balanced Word to Balanced (Sturmian?) Sequence

Let $$E \in \{0,1\}^{n}, n\in \mathbb{N}$$, be a balanced finite word: for every two subwords $$U,V$$ of the same length, the number of $$1$$'s in $$U$$ differs from the number of $$1$$'s in $$V$$ by at most one.

• Can $$E$$ be continued to an infinite balanced sequence?
• Can $$E$$ be continued to an infinite Sturmian sequence? (A subcase of the previous question.)

Furthermore, in both cases, what is the cardinality of the set of possible extensions of $$E$$?

This came up when I tried to solve an exercise, where I have to show that Sturmian sequences are dense in the space of balanced sequences (with regard to the usual topology of symbolic dynamics) - if the the answer to the second question is "yes", than we can take any prefix of length $$n$$ of a balanced sequence, continue it to a Sturmian sequence, and get by the definition of the metric that the distance between the two sequences is $$\leq \frac{1}{2^n}$$.


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# How to Calculate the Volume of a Triangular Prism

Co-authored by wikiHow Staff

Updated: September 17, 2019

It's easy to assume that you'd calculate the volume of a triangular prism the same way you would for a pyramid. However, a triangular prism is a three-sided polyhedron with two parallel triangular bases and three rectangular faces. To calculate the volume, all you have to do is find the area of one of the triangular bases and multiply it by the height of the prism.

### Part 1 of 2: Finding the Area of the Triangle

1. 1
Find the height and width of a triangle base. Look at the triangle and write down the base width and height. For example, your triangle might have a base of 8 cm and a height of 9 cm.[1]
• Keep in mind that you're identifying the height of the triangle, not the entire prism.
• You can use either of the triangular bases, since they should have the same dimensions.
2. 2
Plug the numbers into the formula to find the triangular area. Once you know the width and height of the triangle, put the numbers into the formula for calculating triangular area:[2]
• Area = 1/2 x width x height. You might also see it written as ${\displaystyle V={\frac {1}{2}}bh}$
3. 3
Multiply 1/2 by width by height to get the area of the triangle. In order to find the area of the triangular base for the prism, multiply the width by the height by 1/2. Remember to put the answer in square units because you're calculating area.[3]
• For example, if the base is 8 and the height is 9, your formula will look like ${\displaystyle V={\frac {1}{2}}*8*9}$. The area of the triangle is 36 cm 2.

### Part 2 of 2: Figuring the Volume of the Prism

1. 1
Plug the triangular area into the formula to find the volume of the prism. The area of the triangle is 1 of the 2 numbers you need in order to find the prism's volume. In the formula ${\displaystyle V=bh}$, the triangular area is ${\displaystyle V=b}$.[4]
• To use the earlier example, the formula would be ${\displaystyle V=36*h}$.
2. 2
Identify the height of the prism and put it in the formula. Now you need to find the height of the triangular prism, which is the length of 1 of its sides. For example, the prism may be 16 cm long. Place this number in the ${\displaystyle V=h}$ place of the formula.[5]
• For example, your formula should now look like ${\displaystyle V=36*16}$.
3. 3
Multiply the triangular area by the height of the prism to find the volume. Since you now have all the parts of the equation, multiply the area by the height. The result will be the volume of the triangular prism.[6]
• So, if ${\displaystyle V=36*16}$, the answer is 576 cm 3.

## Community Q&A

Search
• Question
How do I calculate the area of a triangular prism?
To find the surface area of a triangular prism, you would find the area of all the faces, then add them together.
• Question
How can I find the volume of a rectangular prism?
To find the volume of a rectangular prism, multiply the prism's width, height, and length. V = w*h*l
• Question
How do I find the volume of a square pyramid?
Donagan
V = (1/3)(s²)(h), where s is the length of a side of the base, and h is the height.
• Question
How do I calculate volume if there are 3 numbers?
Just times all the numbers together. Once you do, the number you get will be your final answer cubed.
• Question
I need to find the height of a display box shaped like a triangular prism that holds 875 cm3. The bottom of the box measures 35cm by 10 cm. How do I find this?
Donagan
Divide the volume of the prism by the area of the triangle.
• Question
How do I calculate the surface area of a hexagonal prism?
Donagan
Assuming you know the length of each side, multiply the full perimeter by the height. If you need to include the surface area of the two ends of the prism, calculate the area of a hexagonal end, double it, and add that to the lateral surfaces calculated above.
• Question
How can I work out the volume of a triangular prism without the height?
Donagan
You can't.
• Question
How do I calculate the surface area of a triangular prism?
To calculate the surface area, you need to take the sum of the areas of each side. There will be five sides to a triangular prism -- three rectangles and two triangles. Use the formula A=0.5(base*height) to get the area for each triangle. For the rectangles, simply use width*length. After you have the areas for each individual face, add them together. This will give you the total surface area.
• Question
A triangular prism has a volume of 350 cubic meters. If the dimensions are tripled, what is the volume of the new prism?
Donagan
The new volume is nine times the old volume (three dimensions, each tripled).
• Question
How many bases are in a triangular prism?
The top and bottom, which are triangles, are bases. The three rectangles are called lateral faces. A triangular prism has five faces consisting of two triangular bases and three rectangular lateral faces. A base is also a face.
• How do I find the surface area of a triangular prism?
• How can I find the volume of a triangular prism?
• How do I find the volume of a rectangular pyramid?
200 characters left

## Tips

• Ensure that the units of measurement are the same for all parts of the triangular prism before you begin the calculation. For example, if 1 part of the prism is in millimeters and the rest is in centimeters, convert the millimeters to centimeters first.
Thanks!

Co-Authored By:
wikiHow Staff Editor
This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Together, they cited information from 6 references. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article meets our high standards.
Co-authors: 51
Updated: September 17, 2019
Views: 762,092
Categories: Volume
Article SummaryX

To calculate the volume of a triangular prism, measure the width and height of a triangular base, then multiply the base by the height by 1/2 to determine the triangle's area. Next, measure the height of the triangular prism and multiply this by the triangle's area to get the volume. Don't forget to state your answer in cubic units!

Thanks to all authors for creating a page that has been read 762,092 times.

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Annie Rice

Nov 20

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Parkna Rey

Mar 24, 2017

"I had to study for a test on volume and surface area. I wasn't very good at both, so I asked my sister. She tried to help me, but was sick and didn't really know if she was teaching me teaching me right! I was frustrated and couldn't ask anyone else, so I looked it up. I tried the first website I saw, but it didn't help because it had too many confusing equations! So I looked it up again and I tried the second website, yours. It was so easy to understand with the pictures! Thanks."..." more
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Paula Barrows

Mar 8, 2016

"When my son is having trouble understanding the formula to a math problem, inevitably he will understand the straightforward way it is presented here. Finding volume was no exception. We used the Triangular Prism, Rectangular Prism, and Cylinder Volume articles today. All three helped tremendously."..." more
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Anonymous

Mar 1, 2017

"I had a math project and needed to find the volume formula of a triangular prism. I searched numerous websites but couldn't understand. Then after hours of searching, I came across this link and it gave me the solution right away. Thank you very much. This is my next go-to website."..." more
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Ashraful Alam

Feb 28, 2017

"I am a 6th grader. My mom told me to study for the upcoming state test, so I practiced in a book. The book had some questions on triangular prism. I didn't know what to do so I came here. Thank you for the help! You guys are awesome!"..." more
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Anonymous

Dec 6, 2016

"This is a great website. It made it very easy to understand how to find the area of a rectangular prism! "
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Jul 29, 2016

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May 22, 2017

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Nov 28, 2016

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May 3, 2017

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# A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition.

Question:

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

(a) 216

(b) 600

(c) 240

(d) 3125

Solution:

(a) 216

A number is divisible by 3 when the sum of the digits of the number is divisible by 3.

Out of the given 6 digits, there are only two groups consisting of 5 digits whose sum is divisible by 3.

1+2+3+4+5 = 15

0+1+2+4+5 = 12

Using the digits 1, 2, 3, 4 and 5, the 5 digit numbers that can be formed = 5!

Similarly, using the digits $0,1,2,4$ and 5, the number that can be formed $=5 !-4 !\{$ since the first digit cannot be 0$\}$

$\therefore$ Total numbers that are possible $=5 !+5 !-4 !=240-24=216$