Find the Derivative of the Function $g ( x ) = \left( \frac { x + 2 } { x ^ { 2 } + 9 } \right) ^ { 5 }$

question 31

Multiple Choice

Find the derivative of the function. $g ( x ) = \left( \frac { x + 2 } { x ^ { 2 } + 9 } \right) ^ { 5 }$

• A) \(g ^ { \prime } ( x ) = \frac { 5 \left( 9 - 4 x + x ^ { 2 } \right) } { ( 2 + x ) \left( 9 + x ^ { 2 } \right) } \left( \frac { ( 2 + x ) } { \left( 9 + x ^ { 2 } \right) } \right) ^ { 5 }\)
• B) \(g ^ { \prime } ( x ) = \frac { 5 \left( 9 + 4 x - x ^ { 2 } \right) ( 2 + x ) ^ { 4 } } { \left( 9 + x ^ { 2 } \right) ^ { 6 } }\)
• C) \(g ^ { \prime } ( x ) = \frac { 5 \left( 9 - 4 x - x ^ { 2 } \right) ( 2 + x ) ^ { 6 } } { \left( 9 + x ^ { 2 } \right) ^ { 4 } }\)
• D) \(g ^ { \prime } ( x ) = - \frac { 5 \left( 9 - 4 x - x ^ { 2 } \right) ( 2 + x ) ^ { 4 } } { \left( 9 + x ^ { 2 } \right) ^ { 6 } }\)
• E) \(g ^ { \prime } ( x ) = \frac { 5 \left( 9 - 4 x - x ^ { 2 } \right) ( 2 + x ) ^ { 4 } } { \left( 9 + x ^ { 2 } \right) ^ { 6 } }\)

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