Find the Derivative Of $f ( x ) = ( \sin 3 x ) ^ { 2 x }$

Multiple Choice

Find the derivative of $f ( x ) = ( \sin 3 x ) ^ { 2 x }$

A) $f ^ { \prime } ( x ) = ( \sin 3 x ) ^ { 2 x } ( 2 \ln ( \sin 3 x ) + 3 x \cot 3 x )$
B) $f ^ { \prime } ( x ) = ( \sin 3 x ) ^ { 2 x } ( 2 \ln ( \sin 3 x ) + 3 x \tan 3 x )$
C) $f ^ { \prime } ( x ) = ( \sin 3 x ) ^ { 2 x } ( 2 \ln ( \sin 3 x ) + 6 x \cot 3 x )$
D) $f ^ { \prime } ( x ) = ( \sin 3 x ) ^ { 2 x } ( 2 \ln ( \sin 3 x ) + 6 x )$