What is (-2e^{-2x})(xe^{-2x}) ?

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

Apply exponent rule:

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

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

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

x^{4} (3 x^{2})

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

3 e^{- 5}

\frac{( ln ( 0.02 ) ) ^{2}}{π ^{2} + ( ln ( 0.02 ) ) ^{2}}

\frac{2}{6} \cdot \frac{6}{6}

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