## Calculus (3rd Edition)

The term $\frac{\partial x}{\partial v}$ does not appear in the expression of $\frac{\partial f}{\partial u}$.
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 $\frac{\partial f}{\partial u}$.