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

The solution to (e^{-x}ln(x))(xe^{-x}) is e^{-2x}xln(x)

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

e^{- x} e^{- x} = e^{- x - x}

= ln (x) x e^{- x - x}

Add similar elements:

- x - x = - 2 x

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

\frac{1}{4} (2 x^{2} + 1)^{- \frac{1}{5}} (24 x)

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

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

\frac{2}{3}^{3}

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