Answer
$f_x=1/x$
$f_y=-1/y$
Work Step by Step
Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa:
$f_x=\frac{1}{x/y}\times1/y=y/x\times1/y=1/x$
$f_y=\frac{1}{x/y}\times -x/y^2=y/x \times -x/y^2=-1/y$
