What is 4e^{-2x}(1+e^{-x})^{-2} ?

The solution to 4e^{-2x}(1+e^{-x})^{-2} is 4/(e^{2x)(e^{-x}+1)^2}

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simplify 4e^{-2x}(1+e^{-x})^{-2}

simplify

4 e^{- 2 x} (1 + e^{- x})^{- 2}

\frac{4}{e ^{2 x} ( e ^{- x} + 1 ) ^{2}}

Solution steps

4 e^{- 2 x} (1 + e^{- x})^{- 2}

Apply exponent rule:

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

= 4 \cdot \frac{1}{e ^{2 x}} (e^{- x} + 1)^{- 2}

Apply exponent rule:

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

= 4 \cdot \frac{1}{e ^{2 x}} \cdot \frac{1}{( e ^{- x} + 1 ) ^{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 4}{e ^{2 x} ( 1 + e ^{- x} ) ^{2}}

Multiply the numbers:

1 \cdot 1 \cdot 4 = 4

= \frac{4}{e ^{2 x} ( e ^{- x} + 1 ) ^{2}}

\frac{1}{2} e^{- 2.5}

3 - 2 x^{2} + 5

0.18 \cdot e^{- 0}

- e^{2 - 2 t} \cdot (- 2) e^{2 - 2 t}

What is 4e^{-2x}(1+e^{-x})^{-2} ?
The solution to 4e^{-2x}(1+e^{-x})^{-2} is 4/(e^{2x)(e^{-x}+1)^2}