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Popular >

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

Solution

simplify

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

Solution

- e^{- a x - x} x

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

1 \cdot x = x

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

Apply exponent rule:

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

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

= - e^{- a x - x} x

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Frequently Asked Questions (FAQ)

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