$\text { Use the properties of the derivative to find } D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$

question 36

Multiple Choice

$\text { Use the properties of the derivative to find } D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ 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) \(- 6 + 60 t ^ { 4 } - 16 t ^ { 5 }\)

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