Calculate the Derivative of the Function $\left( 4 x ^ { 2 } + 2 x + 2 \right) ^ { - 4 }$

Multiple Choice

Calculate the derivative of the function. $\left( 4 x ^ { 2 } + 2 x + 2 \right) ^ { - 4 }$

A) $g ^ { \prime } ( x ) = \left( - 16 x ^ { 2 } + 8 x + 8 \right) ^ { - 5 }$
B) $g ^ { \prime } ( x ) = - 4 ( 8 x + 2 ) \left( 4 x ^ { 2 } + 2 x + 2 \right) ^ { - 5 }$
C) $g ^ { \prime } ( x ) = - 32 \left( 4 x ^ { 2 } + 2 x + 2 \right) ^ { - 5 }$
D) $g ^ { \prime } ( x ) = - 4 ( 8 x + 2 ) \left( 4 x ^ { 2 } + 2 x + 2 \right)$
E) $g ^ { \prime } ( x ) = - 4 \left( 4 x ^ { 2 } + 2 x + 2 \right) ^ { - 5 }$