1. The problem statement, all variables and given/known data Knowing: y(x,t) = Acos(kx-ωt) Find the partial derivatives of: 1) dy/dt 2) dy/dx 3) d^2y/dt^2 4) d^2y/dx^2 2. Relevant equations 3. The attempt at a solution These are the answers the actual answers: 1) dy/dt = ωAsin(kx-ωt) = v(x,t) of a particle 2) dy/dx = -kAsin(kx-ωt) 3) d^2y/dt^2 = -(ω^2)Acos(kx-ωt) = a(x,t) of a particle 4) d^2y/dx^2 = -(k^2)Acos(ks-wt) now here are my questions: 1) how come when I do the partial derivative of y with respect to t, kx becomes the constant and vice versa with dy/dx, how come ωt becomes the constant? is it because of implicit differentiation? 2) What does it give me to find: dy/dx? the slope? also what about d^2y/dx^2? Thanks for the Help!