Use Logarithmic Differentiation to Find the Derivative of Y $$y = \sqrt [ 3 ] { \frac { ( 3 x + 1 ) ( x + 4 ) ^ { 2 } } { \left( x ^ { 4 } + 6 \right) ( x + 8 ) } }$$

question 534

Multiple Choice

Use logarithmic differentiation to find the derivative of y.
- $$y = \sqrt [ 3 ] { \frac { ( 3 x + 1 ) ( x + 4 ) ^ { 2 } } { \left( x ^ { 4 } + 6 \right) ( x + 8 ) } }$$

• A) \(3 \sqrt [ 3 ] { \frac { ( 3 x + 1 ) ( x + 4 ) ^ { 2 } } { \left( x ^ { 4 } + 6 \right) ( x + 8 ) } } \left( \frac { 3 } { 3 x + 1 } + \frac { 2 } { x + 4 } - \frac { 4 x ^ { 3 } } { x ^ { 4 } + 6 } - \frac { 1 } { x + 8 } \right)\)
• B) \(\frac { 1 } { 3 } \left( \ln ( 3 x + 1 ) + 2 \ln ( x + 4 ) - \ln \left( x ^ { 4 } + 6 \right) - \ln ( x + 8 ) \right)\)
• C) \(\frac { 3 } { 3 x + 1 } + \frac { 2 } { x + 4 } - \frac { 4 x ^ { 3 } } { x ^ { 4 } + 6 } - \frac { 1 } { x + 8 }\)
• D) \(\frac { 1 } { 3 } \sqrt [ 3 ] { \frac { ( 3 x + 1 ) ( x + 4 ) ^ { 2 } } { \left( x ^ { 4 } + 6 \right) ( x + 8 ) } } \left( \frac { 3 } { 3 x + 1 } + \frac { 2 } { x + 4 } - \frac { 4 x ^ { 3 } } { x ^ { 4 } + 6 } - \frac { 1 } { x + 8 } \right)\)

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