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}}

cos^{5} (x) + tan^{5} (x)

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

\frac{d}{d x} (1.2 \cdot sin (2 \cdot x - 0.8 \cdot t + 10))

\frac{ln ( x )}{2}

3 sec^{2} (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}