Answer
$${\frac {\partial z}{\partial t}}={\frac {\partial z}{\partial u}}*{\frac {\partial u}{\partial t}}+{\frac {\partial z}{\partial v}}*{\frac {\partial v}{\partial t}}+{\frac {\partial z}{\partial w}}*{\frac {\partial w}{\partial t}}$$
Work Step by Step
Drawn branch in file