Solved: In Exercises 43 and 44, use the properties of the derivative to find the

Chapter 12, Problem 44

(choose chapter or problem)

In Exercises 43 and 44, use the properties of the derivative to find the following.

(a) r’(t) (b) r’’(t)

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

(d) \(D_{t}[3 r(t)-u(t)]\)

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

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

r(t)=t i+2 sin t j+2 cos t k

\(\mathbf{u}(t)=\frac{1}{t} \mathbf{i}+2 \sin t \mathbf{j}+2 \cos t \mathbf{k}\)

Text Transcription:

u(t)=1/t i+2 sin t j+2 cos t k

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

D_t[3 r(t)-u(t)]

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

D_t[||r(t)||]

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