If Partial derivatives exist and are continuos then function is differentiable

[rshalloo]

Homework Statement

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

Homework 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)

The Attempt at a Solution

I'm guessing that it involves the mean value theorem but I'm not entirely sure :S

 

[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".)