Find the Derivative of the Function $g ( x ) = \left( \frac { x + 6 } { x ^ { 2 } + 7 } \right) ^ { 4 }$

question 123

Multiple Choice

Find the derivative of the function. $g ( x ) = \left( \frac { x + 6 } { x ^ { 2 } + 7 } \right) ^ { 4 }$

• A) \(g ^ { t } ( x ) = \frac { 4 \left( 7 - 12 x + x ^ { 2 } \right) } { ( 6 + x ) \left( 7 + x ^ { 2 } \right) } \left( \frac { 6 + x } { 7 + x ^ { 2 } } \right) ^ { 4 }\)
• B)\(g ^ { t } ( x ) = \frac { 4 \left( 7 - 12 x - x ^ { 2 } \right) ( 6 + x ) ^ { 3 } } { \left( 7 + x ^ { 2 } \right) ^ { 5 } }\)
• C)\(g ^ { t } ( x ) = \frac { 4 \left( 7 + 12 x - x ^ { 2 } \right) ( 6 + x ) ^ { 3 } } { \left( 7 + x ^ { 2 } \right) ^ { 5 } }\)
• D)\(g ^ { t } ( x ) = \frac { 4 \left( 7 - 12 x - x ^ { 2 } \right) ( 6 + x ) ^ { 5 } } { \left( 7 + x ^ { 2 } \right) ^ { 3 } }\)
• E)\(g ^ { t } ( x ) = \frac { 4 \left( 7 - 12 x - x ^ { 2 } \right) ( 6 + x ) ^ { 3 } } { \left( 7 + x ^ { 2 } \right) ^ { 5 } }\).