$\text { Use the Product Rule to differentiate } f ( t ) = t ^ { - 4 } \sin t \text {. }$

question 56

Multiple Choice

$\text { Use the Product Rule to differentiate } f ( t ) = t ^ { - 4 } \sin t \text {. }$

• A) \(f ( t ) = t ^ { - 4 } \cos t - 4 t ^ { 3 } \sin t\)
• B) \(f ^ { t} ( t ) = - t ^ { - 4 } \cos t + 4 t ^ { - 5 } \sin t\)
• C) \(f ^ { t } ( t ) = - t ^ { - 4 } \cos t - 4 t ^ { - 3 } \sin t\)
• D) \(f ^ { t } ( t ) = t ^ { - 4 } \cos t + 4 t ^ { - 5 } \sin t\)
• E) \(f ^ { t} ( t ) = t ^ { - 4 } \cos t - 4 t ^ { - 5 } \sin t\)

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Definitions:

E2 Pathway

A type of bimolecular elimination reaction mechanism where a substrate undergoes deprotonation by a base, leading to the formation of a double bond and the loss of a leaving group in a single step.

E1

A type of unimolecular elimination reaction where the rate determining step involves the removal of a leaving group, forming a carbocation intermediate.

Major Organic Product

In organic chemistry reactions, it is the main product formed, characterized by being present in the greatest amount among products resulting from the conversion of reactants.

Structure

The arrangement or organization of parts within a whole, especially referring to the molecular or atomic arrangement in chemistry.