Chapter 14: Partial Derivatives - Section 14.4 - The Chain Rule - Exercises 14.4 - Page 817: 15

$${\frac {\partial w}{\partial u}}={\frac {\partial w}{\partial x}}*{\frac {\partial x}{\partial u}}+{\frac {\partial w}{\partial y}}*{\frac {\partial y}{\partial u}}+{\frac {\partial w}{\partial z}}*{\frac {\partial z}{\partial u}}$$ $${\frac {\partial w}{\partial v}}={\frac {\partial w}{\partial x}}*{\frac {\partial x}{\partial v}}+{\frac {\partial w}{\partial y}}*{\frac {\partial y}{\partial v}}+{\frac {\partial w}{\partial z}}*{\frac {\partial z}{\partial v}}$$

Drawn branch in the file