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Popular >

simplify xe^{-1/2 x}

Solution

simplify

x e^{- \frac{1}{2} x}

Solution

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

Solution steps

x e^{- \frac{1}{2} x}

Apply exponent rule:

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

= \frac{1}{e ^{\frac{1}{2} x}} x

\frac{1}{e ^{\frac{1}{2} x}} = \frac{1}{e ^{\frac{x}{2}}}

= \frac{1}{e ^{\frac{x}{2}}} x

Multiply fractions:

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

= \frac{1 \cdot x}{e ^{\frac{x}{2}}}

Multiply:

1 \cdot x = x

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

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Frequently Asked Questions (FAQ)

What is xe^{-1/2 x} ?
The solution to xe^{-1/2 x} is x/(e^{x/2)}