Answer
$0$
Work Step by Step
Given: $g(x,y,z)=\sqrt{1+xz}+\sqrt {1-xy}$
Differentiating $\sqrt{1+xz}+\sqrt {1-xy}$ partially with respect to $z$ keeping $x$ and $y$ constant .
$g_z=\dfrac{∂[\sqrt{1+xz}+\sqrt {1-xy}]}{∂z}=\dfrac{x}{2\sqrt{1+xz}}$
Differentiating the above equation partially with respect to $y$ keeping $z$ and $z$ constant .
$g_zy=\dfrac{∂[\dfrac{x}{2\sqrt{1+xz}}]}{∂y}=0$
and
$g_{zyx}=0$
Hence, $f_{zxy}=f_{xyz}=0$
