en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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}}

Popular Examples

(\partial)/(\partial y)(3x^2+y^2)

\frac{\partial}{\partial y} (3 x^{2} + y^{2})

3xy^'+4y=sqrt(x/y)

3 x y^{^{'}} + 4 y = \frac{x}{y}

laplacetransform 1+3t+3t^2 laplace transform

1 + 3 t + 3 t^{2}

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

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

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

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

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)