Chapter 12, Problem 26RE

(a)

To determine

To calculate: The function $r^{\prime }\left(t\right)$ of the provided function $r\left(t\right)=\sin ti+\cos tj+tk$.

(b)

To determine

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

(c)

To determine

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

(d)

To determine

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

(e)

To determine

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

(f)

To determine

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