(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# If Partial derivatives exist and are continuos then function is differentiable

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