Chapter 3.10, Problem 22E

Changing dimensions in a rectangular box Suppose that the edge lengths $x,y,$ and $z$ of a closed rectangular box are changing at the following rates:

$\frac{dx}{dt}=1m/\sec ,\frac{dy}{dt}=-2m/\sec ,\frac{dz}{dt}=1m/\sec$.

Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal length $s=\sqrt{x^2+y^2+z^2}$ are changing at the instant when $x=4,y=3,$ and $z=2$.