What is xe^{-x}((x^{-1})/(-1)) ?

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

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simplify xe^{-x}((x^{-1})/(-1))

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

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

Remove parentheses:

(- a) = - a

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

Apply exponent rule:

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

x x^{- 1} = x^{1 - 1}

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

Subtract the numbers:

1 - 1 = 0

= - \frac{1}{e ^{x}} x^{0}

Apply rule

a^{0} = 1, a \neq = 0

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

Multiply:

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

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

0.5 \cdot a \cdot t^{2} \cdot w^{2}

e^{- \frac{16}{50}}

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

(\frac{8}{5})^{- \frac{1}{2}} \cdot (25)^{3} \cdot (3 2^{\frac{4}{5}})^{- \frac{3}{2}}

5000 e^{- 0.1 \cdot 10.21}

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