Answer
The term $\frac{\partial x}{\partial v}$ does not appear in the expression of $\frac{\partial f}{\partial u}$.
Work Step by Step
According to the chain rule, we have
$$
\frac{\partial f}{\partial u}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial u}+\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}.
$$
So the term $\frac{\partial x}{\partial v}$ does not appear in the expression of $\frac{\partial f}{\partial u}$.
