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

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) \(- 6 + 60 t ^ { 4 } - 16 t ^ { 5 }\)

Understand the significance of sociometric statuses and their implications on children’s social adaptation.

Explore cultural differences in children's social strategies and behaviors.

Comprehend social repair mechanisms and the role of friendships in promoting self-esteem and social competence.

Understand the key factors that influence friendships during middle childhood, including similarity in age, race, and skill level.

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