Partial derivatives question

consider the function:

(2x(x^2-y^2))/(x^2+y^2) ---> (x,y) /= 0

f(x,y) ={

0 ---> (x,y)= 0

Show that fx (x partial) and fy(y partial) exist at (0,0) and determine their value...

I get an x-partial derivative of (2x^4+8x^2y^2-2y^4)/((x^2 + y^2)^2)

I get a y-partial derivative of (-8yx^3)/((x^2+y^2)^2)

I have done them a million times and just keep getting that - how on earth are they supposed to exist at (0,0)??

I was thinking that the numerator would have a factor of (x^2+y^2)^2 but no such luck?

any ideas?