If $f$ Is a Differentiable Function, Find an Expression for the Derivative

question 54

Multiple Choice

If $f$ is a differentiable function, find an expression for the derivative of $y = x ^ { 3 } f ( x )$ .

• A) \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 3 x ^ { 2 } f ( x ) + x ^ { 3 } f ^ { \prime } ( x )\)
• B)
• \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 3 x ^ { 3 } f ( x ) + x ^ { 2 } f ^ { \prime } ( x )\)
• C)
• \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 2 x ^ { 2 } f ( x ) - x ^ { 3 } f ^ { \prime } ( x )\)
• D)
• \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 3 x ^ { 2 } f ( x ) - x ^ { 3 } f ^ { \prime } ( x )\)
• E)
• \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 3 x ^ { 3 } f ( x ) - x ^ { 2 } f ^ { \prime } ( x )\)

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Definitions:

Somatic Nervous System

A part of the peripheral nervous system that is responsible for carrying motor and sensory information both to and from the central nervous system.

Sympathetic Nervous System

The division of the autonomic nervous system that mobilizes the body’s resources during stress and emergencies, preparing the body for action.

Parasympathetic Nervous System

is a division of the autonomic nervous system responsible for rest and digest functions, conserving and restoring energy.

Autonomic Nervous System

The part of the nervous system responsible for the control of bodily functions not consciously directed, such as breathing, the heartbeat, and digestive processes.