Use the properties of the derivative to find

D _ { t } ( \mathbf { r } ( t ) \times \mathbf { u } ( t ) ) \text { given the following }

vector-valued functions.

\begin{array} { l } \mathbf { r } ( t ) = 4 \cos 4 t \mathbf { j } + 4 \sin 4 t \mathbf { k } \\\mathbf { u } ( t ) = \frac { 5 } { t } \mathbf { i } + 4 \cos 4 t \mathbf { j } + 4 \sin 4 t \mathbf { k }\end{array}

A)

\left( \frac { 80 \cos ( 4 t ) } { t } - \frac { 20 \sin ( 4 t ) } { t ^ { 2 } } \right) \mathbf { j } + \left( \frac { 20 \cos ( 4 t ) } { t ^ { 2 } } - \frac { 80 \sin ( 4 t ) } { t } \right) \mathbf { k }

B)

\left( \frac { 80 \cos ( 4 t ) } { t } + \frac { 20 \sin ( 4 t ) } { t ^ { 2 } } \right) \mathbf { j } + \left( \frac { 20 \cos ( 4 t ) } { t ^ { 2 } } + \frac { 80 \sin ( 4 t ) } { t } \right) \mathbf { k }

C)

\left( \frac { 80 \cos ( 4 t ) } { t ^ { 2 } } - \frac { 20 \sin ( 4 t ) } { t } \right) \mathbf { j } + \left( \frac { 20 \cos ( 4 t ) } { t ^ { 2 } } + \frac { 80 \sin ( 4 t ) } { t } \right) \mathbf { k }

D)

\left( \frac { 80 \cos ( 4 t ) } { t } - \frac { 20 \sin ( 4 t ) } { t ^ { 2 } } \right) \mathbf { i } + \left( \frac { 20 \cos ( 4 t ) } { t ^ { 2 } } - \frac { 80 \sin ( 4 t ) } { t } \right) \mathbf { k }

E)

\left( \frac { 80 \cos ( 4 t ) } { t } - \frac { 20 \sin ( 4 t ) } { t ^ { 2 } } \right) \mathbf { j } + \left( \frac { 20 \cos ( 4 t ) } { t ^ { 2 } } + \frac { 80 \sin ( 4 t ) } { t } \right) \mathbf { k }

Find rt(t)⋅rtt(t) given the following vector function. \text { Find } \mathbf { r } ^ { t } ( t ) \cdot \mathbf { r } ^ { tt } ( t ) \text { given the following vector function. } Find rt(t)⋅rtt(t) given the following vector function.

Multiple Choice