## Calculus 8th Edition

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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, $f_{zxy}=f_{xyz}=0$