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

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

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simplify e^{-x}(1/(1+e^x))

simplify

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

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

Solution steps

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

Apply exponent rule:

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

= \frac{1}{e ^{x}} \cdot \frac{1}{e ^{x} + 1}

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

(x^{2} - 17) e^{- x}

\frac{- 50}{10}

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

\frac{- 80}{- 16}