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

The solution to d/(d^2x)(xe^{-x}) is 1/(de^x)

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simplify d/(d^2x)(xe^{-x})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Cancel the common factor:

x

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

Multiply:

d \cdot 1 = d

= \frac{d}{d ^{2} e ^{x}}

Cancel the common factor:

d

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

(2 x) (3 x^{2}) (4 x^{3})

6.7576300000000 \dots \cdot 1 0^{- 13}

0 \cdot e^{- 5 x}

1.6 \cdot 1 0^{- 19} \cdot 16

12000 \cdot 4 π \cdot 1 0^{- 7}