Solved: Using Properties of the Derivative In Exercises 39 and 40, use the properties of
Chapter 12, Problem 40(choose chapter or problem)
Using Properties of the Derivative In Exercises 39 and 40, use the properties of the derivative to find the following.
(a) r’(t)
(b) \(\frac{d}{d t}[3 \mathbf{r}(t)-\mathbf{u}(t)]\)
(c) \(\frac{d}{d t}(5 t) \mathbf{u}(t)\)
(d) \(\frac{d}{d t}[\mathrm{r}(t) \cdot \mathrm{u}(t)]\)
(e) \(\frac{d}{d t}[\mathbf{r}(t) \times \mathbf{u}(t)]\)
(f) \(\frac{d}{d t} \mathbf{r}(2 t)\)
\(\mathbf{r}(t)=t \mathbf{i}+2 \sin t \mathbf{j}+2 \cos t \mathbf{k}\)
\(\mathbf{u}(t)=\frac{1}{t} \mathbf{i}+2 \sin t \mathbf{j}+2 \cos t \mathbf{k}\)
Text Transcription:
d/dt [3r(t)-u(t)]
d/dt (5t)(t)
d/dt [r(t) times u(t)]
d/dt [r(t) times u(t)]
d/dt r(2t)
r(t)=ti+2 sin tj+2 cos tk
u(t)=1/t i+2 sin tj + 2 cos tk
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