\text { Calculate } \frac{\partial^{2} f}{\partial x \partial y}(0,0) \text { and } \frac{\partial^{2} f}{\partial y \partial x}(0,0) \text { for the following function: } f(x, y):=\left\{\begin{array}{l}

x y \frac{x^{2}-y^{2}}{x^{2}+y^{2}}, \quad(x, y) \neq(0,0) \\

0, \quad(x, y)=(0,0)

\end{array}\right. by the definition of partial derivatives.