implicit Partial differentiation

Hi,

I have a problem that has to do with implicit partial differentiation. I was wondering how I could solve it using Jacobian determinants, if not possible, then a straight forward approach is okay. Here we go!

Given:

Prove:

I have a problem finding the two partial terms. This is what I have done:

but I end up with , not

Any suggestions? Thanks!

Re: implicit Partial differentiation

Quote:

Originally Posted by

**gotFermi** Hi,

I have a problem that has to do with implicit partial differentiation. I was wondering how I could solve it using Jacobian determinants, if not possible, then a straight forward approach is okay. Here we go!

Given:

Prove:

I have a problem finding the two partial terms. This is what I have done:

but I end up with

, not

Any suggestions? Thanks!

Your notation doesn't make any sense. I would advise writing each function as z in terms of the other variables, then doing the differentiation.

Re: implicit Partial differentiation

What terms don't make sense? I can change that, I am just copying how my book sells the ideas.

I'll give the rewriting a try, thanks.