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

The derivative of 1/(1+e^{-x)} is (e^{-x})/((1+e^{-x))^2}

What is the first derivative of 1/(1+e^{-x)} ?

The first derivative of 1/(1+e^{-x)} is (e^{-x})/((1+e^{-x))^2}

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{2 x + 1}{x ^{2} + 2 x + 82} d x

x \to 2 lim (4 x^{2})

\frac{d}{d x} (e^{x^{2} - 4} + 4 x + 11)

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

\int (ln (7 x))^{2} d x

What is the derivative of 1/(1+e^{-x)} ?
The derivative of 1/(1+e^{-x)} is (e^{-x})/((1+e^{-x))^2}
What is the first derivative of 1/(1+e^{-x)} ?
The first derivative of 1/(1+e^{-x)} is (e^{-x})/((1+e^{-x))^2}