Answer
$f_x=y^2 \\ f_y=2xy \\f_z=-4z$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ and $z$ as a constant, and vice versa:
$f_x=y^2 ; \\ f_y=2xy; \\f_z=-4z$
