# Homework Help: Partial Derivative of atan(xy/(1+x^2+y^2)^0.5)

1. Nov 24, 2012

### MrWarlock616

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

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

3. 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. :)

2. Nov 24, 2012

### tiny-tim

Hi MrWarlock616!

You can cancel a (1 + x2), top-and-bottom

3. Nov 24, 2012

### MrWarlock616

EDIT: -nvm got it-