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:

Soil Erosion

The process by which soil is removed from the land surface by wind or water flow, often exacerbated by human activity, leading to diminished land fertility.

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An agricultural practice that involves planting rows of trees or shrubs interspersed with crops, to enhance biodiversity and reduce soil erosion.

Minimize Soil Erosion

The implementation of practices and measures aimed at reducing the removal of soil by water, wind, or other erosive forces.