 dayachesi anaku utpannam yokka ardham yokka saaraamsaanni ivvande .
 ganithamloo ,  nijamaina variable yokka function yokka utpannam dani vaadanalo  ( in ‌ putt viluva )  maarpuku sambandhinchi function viluva  ( avut ‌ putt viluva )  yokka maarpuku sunnitatvaanni kolustundi .  utpannaalu calculus yokka praadhimika sadhanam .  udaharanaku ,  kalaniki sambandhinchi kadile vasthuvu yokka sthaanam yokka utpannam vasthuvu yokka veegam :  idi samayam periginappudu vasthuvu yokka sthaanam entha twaraga maarutundo kolustundi .

 enchukunna in ‌ putt viluva oddha oche variable yokka function yokka utpannam ,  adi unikilo unnappudu ,  aa samayamlo function yokka graph ‌ ku tangent Jalor yokka valu .  tangent Jalor anede aa in ‌ putt viluvaku sameepamlo unna function yokka utthama sarala ujjayimpu .  yea kaaranamgaa ,  utpannam tarachugaa  " takshana maarpu raetu " gaaa varninchabadutundi ,  swatanter chararasiki dependant variable ‌ loo takshana maarpu yokka nishpatthi .

 derivative ‌ lanu anek reall variables function ‌ laku saadhaaraneekarinchavachchu .  yea saadhaaraneekaranalo ,  utpannam ooka liinear trance ‌ firmation ‌ gaaa punarnirvachinchabaduthu ,  deeni graph  ( samuchitamaina anuvaadham tarwata )  asalau function yokka graph ‌ ku utthama sarala ujjaayimpugaa umtumdi .  jacobian matrhuka anede swatanter mariyu dependant variables empika dwara ivvabadina praatipadikaku sambandhinchi yea sarala parivartananu suuchinchae matrhuka .  swatanter variables ‌ ku sambandhinchi pakshika utpannaala paranga dheenini lekkinchavachhu .  anek variables yokka nijamaina - viluva function choose ,  jacobian matricks gradient wector ‌ ki taggistundi .

 utpannaanni kanugone prakriyanu bheedam antaruu .  rivers prakriyanu antidiferenciation antaruu .  calculus yokka praadhimika siddhaantam ekikaranato antidiferenciation ‌ ku sambandhinchinadi .  bheedam mariyu yekikarana anede singel - variable calculus ‌ loo remdu praadhimika karyakalapalanu kaligi umtumdi .
 utpannam anede in ‌ putt ‌ loo maarpula aadhaaramga functionla avut ‌ putt ‌ nu marchadaniki sunnitatvaanni koliche ooka function .  udaharanaku ,  ooka vasthuvu yokka sthaanam nirneetha vyavadhilo entha twaraga kadulutundi  ( anagaa ,  samayaaniki sambandhinchi sthaanam yokka utpannam )  anede vasthuvu yokka veegam .