Answer
$f_x=-(x+y)^{-2}$
$f_y=-(x+y)^{-2}$
Work Step by Step
Rewrite the given equation into the form:
$f(x,y)=(x+y)^{-1}$
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:
$f_x=-(x+y)^{-2}$
$f_y=-(x+y)^{-2}$
