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

question 139

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)
• \(\frac { d } { d x } \left( x ^ { 3 } f ( x ) \right) = 3 x ^ { 3 } f ( x ) - x ^ { 2 } f ^ { \prime } ( x )\)

---

Definitions:

Performance Measures

Quantitative indicators used to evaluate the efficiency, effectiveness, and quality of an organization's activities.

Fixed Salary

A pre-determined amount of money paid to an employee at regular intervals, regardless of performance or hours worked.

Car Salesman

An individual who sells new or used cars at the retail level, employing persuasion to inform and convince customers.

Low Sales

A situation where the number of products sold or the volume of services rendered is below expectations or historical averages.