Answer
As a result $f_x=3x^2yz^2$, $f_y=x^3z^2+2z$, $f_z=2x^3yz+2y$.
Work Step by Step
$f(x,y,z)=x^3yz^2+2yz$
In order to find $f_x$ we treat $y$ and $z$ as constants and differentiate with respect to $x$.
$f_x=3x^2yz^2$
The analogous can be done for $f_y$ and $f_z$.
$f_y=x^3z^2+2z$
$f_z=2x^3yz+2y$
