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Popular >

simplify xe^{-(x/2)^2}

Solution

simplify

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

Solution

\frac{x}{e ^{\frac{x ^{2}}{4}}}

Solution steps

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

Apply exponent rule:

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

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

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

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

Multiply fractions:

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

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

Refine

= \frac{x}{e ^{\frac{x ^{2}}{4}}}

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Frequently Asked Questions (FAQ)

What is xe^{-(x/2)^2} ?
The solution to xe^{-(x/2)^2} is x/(e^{\frac{x^2){4}}}