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## Homework Statement

Prove that if ##z=\arctan(\frac{xy}{\sqrt(1+x^2+y^2)})## , then:

##\frac{\partial^2 z}{\partial x \partial y}=\frac{1}{(1+x^2+y^2)^\frac{3}{2}} ##

## Homework Equations

##\frac{d}{d x} (\arctan(x)) = \frac{1}{1+x^2}##

## The Attempt at a Solution

Differentiating z partially w.r.t y, I got:

## \frac{\partial z}{\partial y} = \frac{x^3+x}{(1+x^2+y^2)^\frac{3}{2} (1+x^2+y^2+x^2y^2)} ##

I'm pretty sure my working till here is correct. But differentiating again w.r.t x would be disastrous. Help me please. :)