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