$\text { Use the properties of the derivative to find } D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ vector-valued functions. $\begin{array} { l }
\mathbf { r } ( t ) = 3 t \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 3 t ^ { 3 } \mathbf { j } \
\mathbf { u } ( t ) = 2 \mathbf { i } + 2 t ^ { 2 } \mathbf { j } - 3 t ^ { 3 } \mathbf { k }
\end{array}$
A) $6 t + 60 t ^ { 4 } - 54 t ^ { 5 }$
B) $6 + 60 t ^ { 4 } - 54 t ^ { 5 }$
C) $- 6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
D) $6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
E) $- 6 + 60 t ^ { 4 } - 16 t ^ { 5 }$

Question

$\text { Use the properties of the derivative to find } D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ vector-valued functions. $\begin{array} { l } 
\mathbf { r } ( t ) = 3 t \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 3 t ^ { 3 } \mathbf { j } \
\mathbf { u } ( t ) = 2 \mathbf { i } + 2 t ^ { 2 } \mathbf { j } - 3 t ^ { 3 } \mathbf { k }
\end{array}$
A) $6 t + 60 t ^ { 4 } - 54 t ^ { 5 }$
B) $6 + 60 t ^ { 4 } - 54 t ^ { 5 }$
C) $- 6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
D) $6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
E) $- 6 + 60 t ^ { 4 } - 16 t ^ { 5 }$

Quizplus · Accepted Answer

The Answer of $\text { Use the properties of the derivative to find } D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ vector-valued functions. $\begin{array} { l } 
\mathbf { r } ( t ) = 3 t \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 3 t ^ { 3 } \mathbf { j } \
\mathbf { u } ( t ) = 2 \mathbf { i } + 2 t ^ { 2 } \mathbf { j } - 3 t ^ { 3 } \mathbf { k }
\end{array}$
A) $6 t + 60 t ^ { 4 } - 54 t ^ { 5 }$
B) $6 + 60 t ^ { 4 } - 54 t ^ { 5 }$
C) $- 6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
D) $6 + 60 t ^ { 4 } + 54 t ^ { 5 }$
E) $- 6 + 60 t ^ { 4 } - 16 t ^ { 5 }$