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Popular Calculus >

derivative of 1/(1+e^x)

Solution

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

Solution

- \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}}

Graph

Popular Examples

derivative of (sin(x+1)/(e^x))

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

inverse oflaplace (e^{-4x})/((x-2)^2)

in v erse l a pl a ce \frac{e ^{- 4 x}}{( x - 2 ) ^{2}}

limit as x approaches infinity of (1+c/x)^{2x}

x \to \infty lim ((1 + \frac{c}{x})^{2 x})

limit as x approaches 1 of x^4e^{-x^2}

x \to 1 lim (x^{4} e^{- x^{2}})

derivative of-2xe^{-x}

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

Frequently Asked Questions (FAQ)

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)