I'm studying the function:
$ f(x,y) = \begin{cases} x+y & \text{if } x=0 \text{ or } y=0 \\ 1& \text{if } xy\neq 0 \end{cases}$
The partial derivatives exist in $(0,0)$, and I can prove that directional derivative doesn't exist in $(0,0)$. Now, Is this function differentiable? Why?
Thanks for your help.