Use the properties of the derivative to find vector-valued functions. $D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ $\begin{array} { l }
\mathbf { r } ( t ) = t \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k } \
\mathbf { u } ( t ) = \frac { 5 } { t } \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k }
\end{array}$
A) 2
B) $\frac { 2 } { t }$
C) $2 t$
D) 5
E) 0

Question

Use the properties of the derivative to find vector-valued functions. $D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ $\begin{array} { l } 
\mathbf { r } ( t ) = t \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k } \
\mathbf { u } ( t ) = \frac { 5 } { t } \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k }
\end{array}$
A) 2
B) $\frac { 2 } { t }$
C) $2 t$
D) 5
E) 0

Quizplus · Accepted Answer

The dot product of $\mathbf{r}(t)$ and $\mathbf{u}(t)$ is constant, so its derivative is zero.

Use the Properties of the Derivative to Find Vector-Valued Functions Dt[r(t)⋅u(t)] given the following D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }Dt​[r(t)⋅u(t)] given the following

Use the Properties of the Derivative to Find Vector-Valued Functions $D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$