Use Logarithmic Differentiation to Find $f ^ { \prime } ( x )$

Multiple Choice

Use logarithmic differentiation to find $f ^ { \prime } ( x )$ . $$f ( x ) = \sqrt [ 3 ] { \frac { 6 x + 3 } { 4 + 4 x } }$$

A) $f ^ { \prime } ( x ) = \left( \frac { 6 } { 6 x + 3 } - \frac { 4 } { 4 + 4 x } \right) f ( x )$
B) $f ^ { \prime } ( x ) = \frac { 1 } { 3 } \left( \frac { 6 } { 6 x + 3 } - \frac { 4 } { 4 + 4 x } \right) f ( x )$
C) $f ^ { \prime } ( x ) = \left( \frac { 6 x + 3 } { 4 + 4 x } \right) ^ { - 2 / 3 }$
D) $f ^ { \prime } ( x ) = f ( x ) \left( \frac { 6 x + 3 } { 4 + 4 x } \right) ^ { - 2 / 3 }$