Use the Properties of the Derivative to Find Vector-Valued Functions $D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$

question 65

Multiple Choice

Use the properties of the derivative to find vector-valued functions. $D _ { t } [ \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) ] \text { given the following }$ $\begin{array} { l } \mathbf { r } ( t ) = t \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k } \\\mathbf { u } ( t ) = \frac { 5 } { t } \mathbf { i } + 2 \cos 4 t \mathbf { j } + 2 \sin 4 t \mathbf { k }\end{array}$

• A) 2
• B) \(\frac { 2 } { t }\)
• C) \(2 t\)
• D) 5
• E) 0

---

Definitions:

Different Behaviors

Variations in actions or reactions of individuals or groups in different situations.

Cultures

The growth of microorganisms, cells, or tissues in a specially prepared nutrient environment for study or diagnosis.

Tolerant

The ability or willingness to tolerate the existence of opinions or behavior that one does not necessarily agree with.

Mentally Disturbed

A term indicating that an individual may be experiencing disruptions in their mental health that affect their thinking, behavior, and emotions.