What is 1/(x^2(1-e^{-2x))}(sqrt(x^3)e^{-x}) ?

The solution to 1/(x^2(1-e^{-2x))}(sqrt(x^3)e^{-x}) is 1/(e^xx^{1/2)(-e^{-2x}+1)}

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simplify 1/(x^2(1-e^{-2x))}(sqrt(x^3)e^{-x})

simplify

\frac{1}{x ^{2} ( 1 - e ^{- 2 x} )} (x^{3} e^{- x})

\frac{1}{e ^{x} x ^{\frac{1}{2}} ( - e ^{- 2 x} + 1 )}

Solution steps

\frac{1}{x ^{2} ( 1 - e ^{- 2 x} )} (x^{3} e^{- x})

x^{3} : x^{\frac{3}{2}}

= \frac{1}{x ^{2} ( 1 - e ^{- 2 x} )} x^{\frac{3}{2}} e^{- x}

Apply exponent rule:

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

= \frac{1}{x ^{2} ( - e ^{- 2 x} + 1 )} \cdot \frac{1}{e ^{x}} x^{\frac{3}{2}}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot x ^{\frac{3}{2}}}{x ^{2} ( 1 - e ^{- 2 x} ) e ^{x}}

Multiply:

1 \cdot 1 \cdot x^{\frac{3}{2}} = x^{\frac{3}{2}}

= \frac{x ^{\frac{3}{2}}}{e ^{x} x ^{2} ( - e ^{- 2 x} + 1 )}

Apply exponent rule:

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

\frac{x ^{\frac{3}{2}}}{x ^{2}} = \frac{1}{x ^{2 - \frac{3}{2}}}

= \frac{1}{e ^{x} x ^{- \frac{3}{2} + 2} ( - e ^{- 2 x} + 1 )}

Subtract the numbers:

2 - \frac{3}{2} = \frac{1}{2}

= \frac{1}{e ^{x} x ^{\frac{1}{2}} ( - e ^{- 2 x} + 1 )}

e^{x} \cdot e^{4 x}

34253547.17773 \cdot 4 \cdot 273 \cdot 4.4 \cdot 1 0^{- 6}

π (\frac{16}{πh})^{2}

(f \circ f^{-}) (x)

What is 1/(x^2(1-e^{-2x))}(sqrt(x^3)e^{-x}) ?
The solution to 1/(x^2(1-e^{-2x))}(sqrt(x^3)e^{-x}) is 1/(e^xx^{1/2)(-e^{-2x}+1)}