Problem 1230 (difficulty: 4/10)

Let

\(\displaystyle f(x,y)=\begin{cases} 0 & \text{if $(x,y)=(0,0)$} \\ xy{x^2-y^2 \over x^2+y^2} & \text{otherwise.} \end{cases}\)

\(\displaystyle {\partial^2 f\over \partial y \partial x}(0,0)=? \qquad {\partial^2 f\over \partial x \partial y}(0,0)=?\)

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