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:

Personality Disorders

A group of mental disorders characterized by enduring maladaptive patterns of behavior, cognition, and inner experience, significantly deviating from cultural expectations.

Major Problems

Fundamental or significant issues that are substantial in magnitude and require attention or solutions.

DSM-IV-TR

The fourth edition, text revision of the Diagnostic and Statistical Manual of Mental Disorders, a handbook used by healthcare professionals as the authoritative guide to diagnose mental disorders.

Cluster C

A classification within personality disorders characterized by anxious and fearful behavior, including avoidant, dependent, and obsessive-compulsive personality disorders.