$$z=f\left(x,y\right)=x^{2}\tan^{-1}\left(\frac{y}{x}\right)-y^{2}\tan^{-1}\left(\frac{x}{y}\right)$$
Prove that $$\frac{\partial^{2}f\left(x,y\right)}{\partial x\,\partial y}=\frac{x^{2}-y^{2}}{x^{2}+y^{2}}$$
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Kindly use correct notation so we can understand your question. This is gibberish. – MPW Aug 25 '14 at 18:34
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1Check my edit.. – drhab Aug 25 '14 at 18:38
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What do you mean by partial fraction method? (This is normally a term one finds in integration problems). What have you tried so far? – rogerl Aug 25 '14 at 18:52
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The answer just hinges on performing the derivatives on one of the terms correctly, the other term is the same with the roles of $x$ and $y$ switched. You can also take the derivatives in either order. Start with the first term and see that the $y$ derivative is just:
$\frac{x^3}{y^2 + x^2}$
The answer is straight forward frome there.
amcalde
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