Consider function $f: \mathbb{R}^n \to \mathbb{R}$. Suppose
1) At ${\bf x}_0$, $f({\bf x})$ has partial derivatives ${\bf J}({\bf x}_0)$.
2) ${\bf J}({\bf x})$ is continuous at ${\bf x}_0$.
I know that $f({\bf x})$ is differentiable at ${\bf x}_0$.
Question: Is there a neighborhood of ${\bf x}_0$ on which $f({\bf x})$ is differentiable?
I know $f({\bf x})$ has partial derivatives on a neighborhood of ${\bf x}_0$, however this does not necessarily imply that $f({\bf x})$ is differentiable there.
