Chapter 12.2, Problem 3QCE

Suppose that ${\text{r}}_1\left(0\right)=〈3,2,1〉,{\text{r}}_2\left(0\right)=〈1,2,3〉,{\text{<msup> r <mo> ′ </mo> </msup>}}_1\left(0\right)=〈0,0,0〉,{\text{and <msup> r <mo> ′ </mo> </msup>}}_2\left(0\right)=〈-6,-4,-2〉.$

Use this information to evaluate the derivative of each function at $t=0.$

$\begin{array}{l}\left(\text{a}\right)\text{r}\left(t\right)=2{\text{r}}_1\left(t\right)-{\text{r}}_2\left(t\right)\\ \left(\text{b}\right)\text{r}\left(t\right)=\cos t{\text{r}}_1\left(t\right)+e^{2t}{\text{r}}_2\left(t\right)\\ \left(\text{c}\right)\text{r}\left(t\right)={\text{r}}_1\left(t\right)\times {\text{r}}_2\left(t\right)\\ \left(\text{d}\right)f\left(t\right)={\text{r}}_1\left(t\right)\cdot {\text{r}}_2\left(t\right)\end{array}$