Solution
= Solution
On the nonzero $x$ axis the function equals one, whereas its assigned value at the origin is zero. Therefore $f(x,0)$ does not tend to $f(0,0)$ as $x\to0$. It is not a <continuous function> there, and <differentiability implies continuity> shows
$$
\boxed{f\text{ is not differentiable at }(0,0).}
$$