Let $\mathbf { v } ( t ) = \sin t \mathbf { i } - 2 \cos t \mathbf { j } + t ^ { 2 } \mathbf { k }$

Multiple Choice

Let $\mathbf { v } ( t ) = \sin t \mathbf { i } - 2 \cos t \mathbf { j } + t ^ { 2 } \mathbf { k }$ and $\mathbf { w } ( t ) = 3 \cos t \mathbf { i } + \sin t \mathbf { j } - t ^ { 2 } \mathbf { k }$ Then $\frac { d } { d t } ( \mathbf { v } ( t ) \bullet \mathbf { w } ( t ) )$ is

A) $\cos ( 2 t ) + 4 t ^ { 3 }$
B) $\cos ( 2 t ) - 4 t ^ { 3 }$
C) $- \cos ( 2 t ) - 4 t ^ { 3 }$
D) $- \cos ( 2 t ) + 4 t ^ { 3 }$
E) $2 \cos ( 2 t ) - 4 t ^ { 3 }$