Chapter 13.5, Problem 38ES

Determine whether the statement is true or false. Explain your answer.

If z is a differentiable function of $x_1,x_2,\text{and}{x}_3$ and if $x_i$ is a differentiable function of t for $i=1,2,3,\text{then}z$ is a differentiable function of t and $\frac{dz}{dt}={\displaystyle \underset{i=1}{\overset{3}{\sum }}\frac{\partial z}{\partial x_i}}\frac{d{x}_i}{dt}$