Chapter 12.2, Problem 36E

(a)

To determine

To calculate: The value of $r^{\prime }\left(t\right)$.

(b)

To determine

To calculate: The value of $\frac{d}{dt}\left[3r\left(t\right)-u\left(t\right)\right]$.

(c)

To determine

To calculate: The value of $\frac{d}{dt}\left[\left(5t\right)u\left(t\right)\right]$.

(d)

To determine

To calculate: The value of $\frac{d}{dt}\left[r\left(t\right)·u\left(t\right)\right]$.

(e)

To determine

To calculate: The value of $\frac{d}{dt}\left[r\left(t\right)\times u\left(t\right)\right]$.

(f)

To determine

To calculate: The value of $\frac{d}{dt}\left[r\left(2t\right)\right]$.