Find the Derivative of the Function $$h ( x ) = \left( \frac { \cos x } { 1 + \sin x } \right) ^ { 4 }$$

question 535

Multiple Choice

Find the derivative of the function.
- $$h ( x ) = \left( \frac { \cos x } { 1 + \sin x } \right) ^ { 4 }$$

• A) \(\left( - \frac { 4 \sin x } { \cos x } \right) \left( \frac { \cos x } { 1 + \sin x } \right) ^ { 3 }\)
• B) \(4 \left( \frac { \cos x } { 1 + \sin x } \right) ^ { 3 }\)
• C) \(- 4 \left( \frac { \sin x } { \cos x } \right) ^ { 3 }\)
• D) \(\frac { - 4 \cos ^ { 3 } x } { ( 1 + \sin x ) ^ { 4 } }\)

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Definitions:

Sensory Register

The part of the memory system where sensory information is stored for a very short period of time.

Visual Images

Mental representations of objects, scenes, or events produced by the brain, often used in memory and creative processes.

Half Second

A very short time interval, specifically one half of a second, often used to measure quick, precise moments.

Executive Processes

Higher-order cognitive processes involved in the planning, initiation, sequence, and monitoring of complex goal-directed behavior.