$\text { Find the derivative of the function } \frac { \sin x } { 2 x + \cos x } \text {. Simplify your answer. }$

question 99

Multiple Choice

$\text { Find the derivative of the function } \frac { \sin x } { 2 x + \cos x } \text {. Simplify your answer. }$

• A)
• \(\frac { 2 x \cos x - \cos ^ { 2 } x - 2 \sin x + \sin ^ { 2 } x } { ( 2 x + \cos x ) ^ { 2 } }\)
• B)
• \(\frac { \cos x } { ( 2 - \sin x ) ^ { 2 } }\)
• C) \(\frac { \cos x } { 2 - \sin x }\)
• D) \(\frac { 1 + 2 x \cos x - 2 \sin x } { ( 2 x + \cos x ) ^ { 2 } }\)
• E) \(\frac { 2 x \cos x + \cos ^ { 2 } x - 2 \sin x - \sin ^ { 2 } x } { ( 2 x + \cos x ) ^ { 2 } }\)

---

Definitions:

Mantle-Derived Magmas

Magma that originates from the melting of the Earth's mantle, leading to volcanic activity.

Continental Crust

The layer of igneous, sedimentary, and metamorphic rocks that forms the continents and continental shelves, characterized by its thickness and composition distinct from oceanic crust.

Mafic Basalt

A type of basaltic rock that is rich in magnesium and iron, characterized by its dark color and low silica content.

Decompression Melting

The melting of rock due to a decrease in pressure as it rises towards the Earth's surface, a common mechanism at mid-ocean ridges and mantle plumes.