Find the Derivative of the Function $f ( x ) = x ^ { 4 } ( 3 + 3 x ) ^ { 3 }$

Multiple Choice

Find the derivative of the function. $f ( x ) = x ^ { 4 } ( 3 + 3 x ) ^ { 3 }$

A) $f ^ { \prime } ( x ) = x ^ { 2 } ( 3 + 3 x ) ^ { 3 } ( 12 + 21 x )$
B) $f ^ { \prime } ( x ) = 3 x ^ { 4 } ( 3 + 3 x ) ^ { 2 } ( 12 + 21 x )$
C) $f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 3 } ( 12 + 21 x )$
D) $f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 2 } ( 12 + 21 x )$
E) $f ^ { \prime } ( x ) = x ^ { 3 } ( 3 + 3 x ) ^ { 2 } ( 12 + 3 x )$