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?

Question

anonymous · Answer

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..

primeralph · Answer

Someone tag me?

primeralph · Answer

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

primeralph · Answer

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?

primeralph · Answer

@Dmitt  Can't stay her forever.