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

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

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

simplify

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

2 (x - 1)

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

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

Factor

e^{x} x - e^{x} : e^{x} (x - 1)

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

Cancel the common factor:

e^{x}

= 2 (x - 1)

- 2 k e^{- 2 (0)}

e^{- s t} (t - 1)^{2}

e^{- t} d x

\frac{3}{34}

- 3 A^{3} (4 A^{4})