Find the Derivative of the Function $$g ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 6 x }$$

question 86

Multiple Choice

Find the derivative of the function.
- $$g ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 6 x }$$

• A) \(g ^ { \prime } ( x ) = \frac { 6 x ^ { 2 } - 10 x - 30 } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• B) \(g ^ { \prime } ( x ) = \frac { x ^ { 4 } + 6 x ^ { 3 } + 5 x ^ { 2 } + 30 x } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• C) \(g ^ { \prime } ( x ) = \frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 30 x } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• D) \(g ^ { \prime } ( x ) = \frac { 4 x ^ { 3 } + 18 x ^ { 2 } + 10 x + 30 } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)

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