What is the derivative of x 2 e x ?

Differentiate using the Quotient Rule which states that d d x [ f ( x ) g ( x ) ] is g ( x ) d d x [ f ( x ) ] − f ( x ) d d x [ g ( x ) ] g ( x ) 2 where f ( x ) = x 2 and g ( x ) = e x e x d d x [ x 2 ] − x 2 d d x [ e x ] ( e x ) 2 Differentiate using the Power Rule which states that d d x [ x n ] is n x n − 1 where n=2. e x ( 2 x ) − x 2 d d x [ e x ] ( e x ) 2 Differentiate using the Exponential Rule which states that d d x [ a x ] is a x ln ⁡ ( a ) where a=e. e x ( 2 x ) − x 2 e x ( e x ) 2 Simplify. 2 x e − x − x 2 e − x

Answered: "What is the derivative of x 2 e..."

abiejose55d

Answered question

2022-05-02

What is the derivative of

\frac{x^{2}}{e^{x}}

Answer & Explanation

kweefomucy9

Beginner2022-05-03Added 13 answers

Differentiate using the Quotient Rule which states that

\frac{d}{d x} [\frac{f (x)}{g (x)}]

\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{g (x)^{2}}

where

f (x) = x^{2}

and

g (x) = e^{x}

\frac{e^{x} \frac{d}{d x} [x^{2}] - x^{2} \frac{d}{d x} [e^{x}]}{(e^{x})^{2}}

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

n x^{n - 1}

where n=2.

\frac{e^{x} (2 x) - x^{2} \frac{d}{d x} [e^{x}]}{(e^{x})^{2}}

Differentiate using the Exponential Rule which states that

\frac{d}{d x} [a^{x}]

a^{x} \ln (a)

where a=e.

\frac{e^{x} (2 x) - x^{2} e^{x}}{(e^{x})^{2}}

Simplify.

2 x e^{- x} - x^{2} e^{- x}

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