Consider a box with dimensions x, y, and z. x is changing at a rate of 1 m/s, y at -2 m/s and z at 1 m/s. Find the rate that the volume, surface area and diagonal length (s=√x2+y2+z2) are changing at the instant when x=4, y=3 and z=2. I know I need to use to product rule. But my teacher didn't bother to teach it to us how to do it with three variables (ex. xyz for the volume). So I'm having trouble figuring out how to start this problem.
