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Popular >

simplify (e^{-x})(-xe^{-x})

Solution

simplify

(e^{- x}) (- x e^{- x})

Solution

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

Solution steps

(e^{- x}) (- x e^{- x})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{x}} (- e^{- x} x)

Remove parentheses:

(- a) = - a

= - \frac{1}{e ^{x}} x e^{- x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot x e ^{- x}}{e ^{x}}

Multiply:

1 \cdot x = x

= - \frac{e ^{- x} x}{e ^{x}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

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

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

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Frequently Asked Questions (FAQ)

What is (e^{-x})(-xe^{-x}) ?
The solution to (e^{-x})(-xe^{-x}) is -x/(e^{2x)}