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:

Vitamin E

A fat-soluble antioxidant vitamin that helps protect cells from oxidative damage.

Blood Clot

A mass formed by the coagulation of blood to stop bleeding in response to an injury or cut.

Vitamin K

A fat-soluble vitamin important for blood clotting and bone health, found in green leafy vegetables, vegetable oils, and some fruits.

Fat-Soluble Vitamin

Vitamins that dissolve in fats and oils, can be stored in the body's fatty tissue and liver, including vitamins A, D, E, and K.