Use Logarithmic Differentiation to Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$

question 61

Multiple Choice

Use logarithmic differentiation to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . $y = \left( x ^ { 3 } + x \right) \sqrt { x ^ { 3 } + 6 }$ ?

• A) \(\left( \frac { 3 x ^ { 2 } + 1 } { x ^ { 3 } + x } + \frac { 3 x ^ { 2 } } { 2 x ^ { 3 } + 12 } \right)\)
• B) \(\left( x ^ { 3 } + x \right) \sqrt { x ^ { 3 } + 6 } \left( \frac { 1 } { x ^ { 3 } + x } + \frac { 1 } { 2 \left( x ^ { 3 } + 6 \right) } \right)\)
• C) \(\left( x ^ { 3 } + x \right) \sqrt { x ^ { 3 } + 6 } \left( \frac { 3 x ^ { 2 } + 1 } { x ^ { 3 } + x } + \frac { 3 x ^ { 2 } } { 2 \left( x ^ { 3 } + 6 \right) } \right)\)
• D) \(\left( 3 x ^ { 2 } + 1 \right) \left( \frac { 3 x ^ { 2 } + 1 } { x } + \frac { 3 x ^ { 2 } } { 2 x ^ { 3 } + 12 } \right)\)
• E) \(3 x ^ { 2 } \sqrt { x ^ { 3 } + 12 } \left( \frac { 3 x ^ { 2 } + 1 } { x ^ { 3 } + x } + \frac { x ^ { 2 } } { 2 x ^ { 3 } + 6 } \right)\)

Discern the psychological and health impacts of eating disorders.

Identify the factors contributing to the success or failure of weight loss programs.

Evaluate the role of behavior modification in weight management.

Understand the relationship between diet composition and weight management.

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Definitions:

Motor Coordination

The ability to execute smooth, accurate, and controlled motor responses, often involving the synchronization of movement and sensory feedback.

Addiction

Addiction is a chronic disorder characterized by compulsive engagement in rewarding stimuli, despite adverse consequences, often leading to physical and psychological dependence.

Depressant

A substance that reduces arousal or stimulation in various areas of the brain, often used to treat anxiety and sleep disorders.

Social Interactions

The processes by which individuals act and react to those around them.