Chapter 12.2, Problem 34E

a.

To determine

Verify that ur is continuous on [a, b] when u and r are continuous on [a, b].

b.

To determine

Verify that ur is differentiable on [a, b] when u and r are both differentiable on [a, b] and also verify that $\frac{d}{dt}\left(ur\right)=r\frac{du}{dt}+u\frac{dr}{dt}$.