1
$\begingroup$

Suppose $f: R^n\to R^m$ n > 1 s.t. all the partial derivatives are discontinuous at point a. Is the function differentiable at a? I would think not however, I know of an example in R that works, so I am wondering how this works with the linear operator of differentiability.

$\endgroup$
1
$\begingroup$

Hint: Let $f$ be your example in one variable. Think about $f(x)+f(y).$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.