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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x}{1 + x ^{\frac{3}{2}}})

\frac{\partial}{\partial x} (\frac{y}{x})

\int_{0}^{x} t^{2} + t^{4} d t

\frac{d y}{d x} = y^{2} - 4

\frac{\partial}{\partial x} (sin (5 π x + 2 y))

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