Question: Find \(\frac{{{\partial }^{2}}f\left( 0,0 \right)}{\partial y\partial x}\) and \(\frac{{{\partial }^{2}}f\left( 0,0 \right)}{\partial x\partial y}\) for the function

\[f\left( x,y \right)=\left\{ \begin{aligned} & xy\frac{\left( {{x}^{2}}-{{y}^{2}} \right)}{{{x}^{2}}+{{y}^{2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\left( x,y \right)\ne \left( 0,0 \right) \\ & \,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( x,y \right)=\left( 0,0 \right) \\ \end{aligned} \right.\]