Answer
$f_x=\frac{1}{y}$, $f_y=\frac{-x}{y^2}$.
Work Step by Step
$f(x,y)=\frac{x}{y}$
In order to find $f_x$ we treat $y$ as a constant and differentiate with respect to $x$.
$f_x=\frac{1}{y}$
In order to find $f_y$ we treat $x$ as a constant and differentiate with respect to $y$.
$f_y=\frac{-x}{y^2}$
