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

Multiple Choice

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