# Implicit function theorem

1. Aug 4, 2007

### jdstokes

1. The problem statement, all variables and given/known data

Understanding the proof of the implicit function theorem.

2. Relevant equations

May assume the inverse function theorem.

3. The attempt at a solution

I'm following a proof given on the net:

http://ocw.mit.edu/NR/rdonlyres/Mat...E8-2EFB-493C-8201-4743AA4EB1EE/0/chapter4.pdf

since I'm unhappy with my lecturer's explanation.

The only thing I'm not clear about in this proof is the fact that the inverse function h is of the form $h(x,y) = (x,k(x,y))$ for some differentiable function k. Apparently this is clear but I just don't see it.

Any help would be appreciated.