Find the Derivative $$y = 6 x ^ { 2 } e ^ { - x }$$

question 99

Multiple Choice

Find the derivative.
- $$y = 6 x ^ { 2 } e ^ { - x }$$

• A) \(6 x e ^ { - x } ( 2 - x )\)
• B) \(12 x e ^ { - x } ( 1 - x )\)
• C) \(6 \mathrm { xe } ^ { - \mathrm { x } } ( \mathrm { x } + 2 )\)
• D) \(6 \mathrm { xe } ^ { \mathrm { x } } ( 2 - \mathrm { x } )\)

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Definitions:

Law of Demand

States that, all other factors being equal, as the price of a good increases, demand for that good decreases, and vice versa.

Quantity Demanded

The amount of a good or service that consumers are willing and able to purchase at a specific price.

Price

The amount of money required to purchase a good or service, determined by factors such as supply and demand.

Normal Good

A type of good for which demand increases when income increases, demonstrating a direct relationship between income and demand.