Let $\mathbf { v } ( t ) = \sin t \mathbf { i } + \cos t \mathbf { j } + t \mathbf { k }$

Multiple Choice

Let $\mathbf { v } ( t ) = \sin t \mathbf { i } + \cos t \mathbf { j } + t \mathbf { k }$ and $\mathbf { w } ( t ) = \sin t \mathbf { i } + \cos t \mathbf { j } + t ^ { 3 } \mathbf { k }$ Then $\frac { d } { d t } ( \mathbf { v } ( t ) \bullet \mathbf { w } ( t ) )$ is

A) $4 t ^ { 3 }$
B) $4 t ^ { 5 }$
C) $- 4 t ^ { 3 }$
D) $- 3 t ^ { 3 }$
E) $3 t ^ { 3 }$