Find the Derivative of the Function $t ( x ) = \frac { \cot x } { 4 + 8 \sec x }$

Multiple Choice

Find the derivative of the function. $t ( x ) = \frac { \cot x } { 4 + 8 \sec x }$

A) $t ^ { \prime } ( x ) = - \frac { ( 4 - 8 \sec x ) \csc ^ { 2 } x + 8 \sec x } { ( 4 - 8 \sec x ) ^ { 2 } }$
B) $t ^ { \prime } ( x ) = - \frac { ( 4 + 8 \sec x ) \csc ^ { 2 } x + 8 \sec x } { ( 4 + 8 \sec x ) ^ { 2 } }$
C) $t ^ { \prime } ( x ) = \frac { ( 4 + 8 \sec x ) \csc ^ { 2 } x + 8 \sec x } { ( 4 + 8 \sec x ) ^ { 2 } }$
D) $t ^ { \prime } ( x ) = - \frac { ( 4 + 8 \sec x ) \csc ^ { 2 } x + 8 \sec x } { ( 4 - 8 \sec x ) ^ { 2 } }$
E) $t ^ { \prime } ( x ) = - \frac { ( 4 - 8 \sec x ) \csc ^ { 2 } x - 8 \sec x } { ( 4 - 8 \sec x ) ^ { 2 } }$