I'm trying to show:
Let $f:A\subset \mathbb{R}^2 \to \mathbb{R}$, if the partial derivative $d_{e1}f$ exists and is continuous in open set $V\subset A$ around $x_0$ and $d_{e2}f$ exists, then $f$ is differentiable in $x_0$.
I know that if the partial derivatives exists and it's continuous then $f$ is differentiable, but I can't use this result.
Thanks for your help.