Answer
$f_x=-yz \space e^{-xyz}$;
$f_y=-xz \space e^{-xyz}$;
$f_z=-xy \space e^{-xyz}$
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:
$f_x=-yz \space e^{-xyz}$;
$f_y=-xz \space e^{-xyz}$;
$f_z=-xy \space e^{-xyz}$
