If $\mathbf { u } ( t ) = \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + 4 t ^ { 4 } \mathbf { k }$

question 1

Short Answer

If $\mathbf { u } ( t ) = \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + 4 t ^ { 4 } \mathbf { k }$ and $\mathbf { v } ( t ) = t \mathbf { i } - \cos t \mathbf { j } + \sin t \mathbf { k }$ , find $\frac { d } { d t } [ \mathbf { u } ( t ) \cdot \mathbf { v } ( t ) ]$ .

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