If Partial derivatives exist and are continuos then function is differentiable

1. Sep 25, 2011

rshalloo

1. The problem statement, all variables and given/known data
Hi I'm just looking for a link to the proof of this theorem:
if the partial derivatives of function f exist and are continuous at a point then the function is differentiable there

Or even the name would be helpful
Its not a homework assignment per say, just something that our lecturer said mentioned in passing but never gave a proof of and I would like it just for the sake of completeness :P

2. Relevant equations

Well I think the newton quotient is [ f(a+h,b+k) -(h)f(a,b+k)-(k)f(a+h,b) ]/Sqrt[h^2+k^2]
(for 2 variables anyway)

3. The attempt at a solution
I'm guessing that it involves the mean value theorem but I'm not entirely sure :S

2. Sep 25, 2011

HallsofIvy

Any good Calculus text will have that proof- but I think it is too long and complicted to be given here.

(By the way, the phrase is "per se"- "of itself".)