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/Mathematics/18-994Fall-2004/5A4796E8-2EFB-493C-8201-4743AA4EB1EE/0/chapter4.pdf [Broken] 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 [itex]h(x,y) = (x,k(x,y))[/itex] for some differentiable function k. Apparently this is clear but I just don't see it. Any help would be appreciated.