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

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

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expand (2/(1+e^{-2x)}-1)^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = \frac{2}{1 + e ^{- 2 x}}, b = 1

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

Simplify

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

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

f^{'} (x) (x^{2} - 2 x)^{5}

\frac{d x}{d} (x = 200 - 2 y)

1125 - 200 \cdot (75 - x)^{2} d x

\frac{18.6}{( 1 - 3 x ) ^{2}}

A! B +! A B (C + C)

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