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

question 22

Multiple Choice

Use logarithmic differentiation to find $f ^ { \prime } ( x )$ . $f ( x ) = \sqrt [ 8 ] { \frac { 6 x + 5 } { 8 + 6 x } }$

• A) \(f ^ { \prime } ( x ) = \frac { 1 } { 8 } \left( \frac { 6 } { 6 x + 5 } - \frac { 6 } { 8 + 6 x } \right) f ( x )\)
• B) \(f ^ { \prime } ( x ) = f ( x ) \left( \frac { 6 x + 5 } { 8 + 6 x } \right) ^ { - 7 / 8 }\)
• C) \(f ^ { \prime } ( x ) = \left( \frac { 6 } { 6 x + 5 } - \frac { 6 } { 8 + 6 x } \right) f ( x )\)
• D) \(f ^ { \prime } ( x ) = \left( \frac { 6 x + 5 } { 8 + 6 x } \right) ^ { - 7 / 8 }\)

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