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Popular >

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

Solution

simplify

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

Solution

- \frac{x ^{3}}{e ^{x^{2}}}

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x x^{2} = x^{1 + 2}

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

Add the numbers:

1 + 2 = 3

= - \frac{1}{e ^{x^{2}}} x^{3}

Multiply fractions:

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

= - \frac{1 \cdot x ^{3}}{e ^{x^{2}}}

Multiply:

1 \cdot x^{3} = x^{3}

= - \frac{x ^{3}}{e ^{x^{2}}}

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Frequently Asked Questions (FAQ)

What is xe^{-x^2}*(-x^2) ?
The solution to xe^{-x^2}*(-x^2) is -(x^3)/(e^{x^2)}