multivariable calculus - A problem from partial derivatives

$$f(x,y)=\begin{cases}
(x-y)^2\sin\frac1{x-y}&x\ne y\\0&x=y\end{cases}$$

I have to show that the first-order partial derivatives exist for $f$ at each point $(x,y)\in\mathbb R^2$.

First I showed it for all $(x,x)$. There, very easily, it can be shown that the partial derivatives exist and are 0. But I could not proceed with the rest of the plane.