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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

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