What is e^{-x}*ln(1/x) ?

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

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simplify e^{-x}*ln(1/x)

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot ln (\frac{1}{x}) = ln (\frac{1}{x})

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

Simplify

ln (\frac{1}{x}) : - ln (x)

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

Apply the fraction rule:

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

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

8.854 \cdot 1 0^{- 12} (\frac{0.00025}{0.006})

40 (1.661 \cdot 1 0^{- 27})

\frac{1}{( 2 π 4.32 )} e^{(- \frac{1}{2} (0.41481))}

e^{- 3 x} \cdot (e^{- 3 x} - 3 x e^{- 3 x})

3 (c i s \frac{π}{4}) \cdot 5 (c i s \frac{π}{2})