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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

\frac{1}{2} e^{j θ} \cdot \frac{1}{2} e^{- j θ}

\frac{( k + 1 ) ^{k}}{k ^{k}}

t^{2} cos (h) (2 t)

e^{- l n ∣ x - 1 ∣}

(2 x - 1) (2 x x - 1)

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