Answer
$f_{x}(x,y,z)=18x^{2}-2xy^{2}$
$f_{y}(x,y,z)=-2x^{2}y+5y^{4}$
$f_{z}(x,y,z)=0$
$f_{yz}(x,y,z)=0$
Work Step by Step
$f_{x}(x,y,z)=18x^{2}-2xy^{2}$
$f_{y}(x,y,z)=-2x^{2}y+5y^{4}$
$f_{z}(x,y,z)=0$
Differentiate $f_{y}(x,y,z)$ with respect to z to get $f_{yz}(x,y,z)$
$f_{yz}(x,y,z)=0$