Question

Can anyone derive dz/dt=(∂z/∂x)(dx/dt)+(∂z/∂y)(dy/dt). How can∂ cancel out with d. Aren't they not the same?

Answer 1

Are you certain it isn't meant to be...
\[\frac{ dz }{ dt }= \frac{ \delta z }{ \delta x } \frac{ \delta x }{ \delta t } + \frac{ \delta z }{ \delta y }\frac{ \delta y }{ \delta t }?\]
that would make more sense as it would be the sums of partial differential equations..

Answer 2

Someone tag me?

Answer 3

@Dmitt That's a good question.
I had the same question when I was in high school. Hold on.

Answer 4

The proof I can generate deals with taking the impression of a curve on another. That's the way partials work.
How good is your vector calculus?

Answer 5

@Dmitt Can't stay her forever.