What is simplify-1/2 e^{-x}(e^{2x}-1) ?

The solution to simplify-1/2 e^{-x}(e^{2x}-1) is -(e^{2x}-1)/(2e^x)

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simplify-1/2 e^{-x}(e^{2x}-1)

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

(2 16 - x^{2}) (x 16 - x^{2})

\frac{23}{2}

e^{- b x^{2}} \cdot e^{- b x^{2}}

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