Answer
$f_x=\frac{y-x}{(x+y)^3}$, $f_y=\frac{-2x}{(x+y)^3}$.
Work Step by Step
$f(x,y)=\frac{x}{(x+y)^2}$
In order to find $f_x$ we treat $y$ as a constant and differentiate with respect to $x$.
$f_x=\frac{(x+y)^2-2x{(x+y)}}{(x+y)^4}=\frac{y-x}{(x+y)^3}$
In order to find $f_y$ we treat $x$ as a constant and differentiate with respect to $y$.
$f_y=\frac{-2x}{(x+y)^3}$
