What is (d^2)/(d^2x)(e^{-x})ln(x) ?

The solution to (d^2)/(d^2x)(e^{-x})ln(x) is (ln(x))/(e^xx)

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simplify (d^2)/(d^2x)(e^{-x})ln(x)

simplify

\frac{d ^{2}}{d ^{2} x} (e^{- x}) ln (x)

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

Solution steps

\frac{d ^{2}}{d ^{2} x} (e^{- x}) ln (x)

Apply exponent rule:

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

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

Multiply fractions:

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

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

Cancel the common factor:

d^{2}

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

Multiply:

1 \cdot ln (x) = ln (x)

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

4 π \cdot 1 0^{- 7} \cdot 20 \cdot \frac{1}{2 \cdot 0.02}

(e^{0.5 x + 1})^{2}

(10) (8.85 x 1 0^{- 12}) cos (- 5 0^{\circ})

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

What is (d^2)/(d^2x)(e^{-x})ln(x) ?
The solution to (d^2)/(d^2x)(e^{-x})ln(x) is (ln(x))/(e^xx)