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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Polymer

A large molecule or macromolecule composed of many repeated subunits.

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The process through which one or more substances are changed into one or more different substances through the rearrangement, removal, replacement, or addition of atoms.

Major Organic Product

The primary chemical compound formed in the highest yield during an organic reaction.