A) $\frac { d w } { d t } = 8 t ^ { 8 } - \sqrt { 1 - t ^ { 2 } }$

question 50

Multiple Choice

$\text { Let } w = x y \cos z \text {, where } x = t ^ { 3 } , y = t ^ { 5 } \text {, and } z = \arccos t \text {. Find } \frac { d w } { d t } \text {. }$

• A) \(\frac { d w } { d t } = 8 t ^ { 8 } - \sqrt { 1 - t ^ { 2 } }\)
• B) \(\frac { d w } { d t } = 8 t ^ { 8 } + \sqrt { 1 - t ^ { 2 } }\)
• C) \(\frac { d w } { d t } = t ^ { 8 } \left( 8 + \sqrt { 1 - t ^ { 2 } } \right)\)
• D) \(\frac { d w } { d t } = 9 t ^ { 8 }\)
• E) \(\frac { d w } { d t } = t ^ { 8 } \left( 8 - \sqrt { 1 - t ^ { 2 } } \right)\)

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Definitions:

Parallel Play

A developmental stage in early childhood where children play next to each other without interacting.

Intellectual Development

The process of developing cognitive abilities, including thinking, problem-solving, and decision-making skills.

Socialization

The process by which individuals learn and adopt the norms, values, and behaviors appropriate to their society or social group.

Sensorimotor Activity

The phase in early child development where learning occurs through sensory experiences and motor activities.