Solved: In Exercises 23 and 24, find the following

Chapter 12, Problem 23

(choose chapter or problem)

In Exercises 23 and 24, find the following.

(a) \(\mathbf{r}^{\prime}(t)\)

(b) \(\mathbf{r}^{\prime \prime}(t)\)

(c) \(D_{t}[\mathbf{r}(t) \cdot \mathrm{u}(t)]\)

(d) \(D_{t}[\mathbf{u}(t)-2 \mathbf{r}(t)]\)

(e) \(D_{t}[\|\mathbf{r}(t)\|]\),     t > 0

(f) \(D_{t}[\mathbf{r}(t) \times \mathbf{u}(t)]\)

r(t) = 3ti + (t-1)j,       \(\mathbf{u}(t)=t \mathbf{i}+t^{2} \mathbf{j}+\frac{2}{3} t^{3} \mathbf{k}\)

Text Transcription:

r^prime (t)

r^prime prime (t)

D_t [r(t) cdot u(t)]

D_t [u(t) - 2r(t)]

D_t [|r(t)|]

D_t [r(t) times u(t)]

u(t) = ti + t^2 j + 2/3 t^3 k