Determine fxy when f(x,y) = 2xarctan(y/x)

In my work, I have

fx = 2x(-y/(x^2+y^2)) + 2arctan(y/x)

I think I've gotten that right. Now, when I have solve further to get fxy I have:

fxy = 2x [(-x^2 + y^2)/(x^2 + y^2)^2] + 2[-x/(x^2+y^2)]

Upon further simplifying I ultimately get [2x^2+2xy^2]/[(x^2 + y^2)^2] Which isn't an answer choice. I've done this problem over multiple times to always get near an answer choice, but never a direct answer. I think I'm just making too many errors on the second part of the problem.

I know it is a lot of work to write out, but help would be greatly appreciated. Thanks in advanced.

Sorry Zach ;

fx = 2 arctan ( y / x ) + 2x ( (-y/x²) / [ 1 + (y/x)² ] ) = 2 arctan (y / x) - 2xy / [ x² + y² ]

fxy = 2x / [ x² + y² ] - 2 x / [ x² + y² ] + 4 xy² / [ x² + y² ]² = 4xy² / [ x² + y² ]²