Let the function $f$ be: $$ f : \mathbb{R}^{2} \longrightarrow \mathbb{R}, \quad \max (x, y):=\left\{\begin{array}{ll} x & \text { for } x \geq y \\ y & \text { for } x<y \end{array}\right. $$
I am now trying to prove for which values $f$ is differentiable. As I am finding many examples such as $\max(x,0)$ for which $f$ is not differentiable I am stuck finding an approach for the other way.
Any help is much appreciated.