Finding second partial derivatives with arctan

Question

I have a question saying Find all second partial derivatives of $z=arctan(\frac{x+y}{1-xy})$. For the first derivative with respect to x I used u substitution and wound up with $$ \frac{1}{1+u^2}*\frac{1+y^2}{(1-xy)^2}$$ Putting back in the value for u, I was left with what was a nightmare to simplify and wasn't able to do anything with it. The answer for Zxx is supossed to be $\frac{-2x}{(1+x^2)^2}$