What is (\partial)/(\partial x)(1/(1+e^{-w^Tx)}) ?

The answer to (\partial)/(\partial x)(1/(1+e^{-w^Tx)}) is (e^{-xw^T}w^T)/((1+e^{-xw^T))^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(1/(1+e^{-w^Tx)})

\frac{\partial}{\partial x} (\frac{1}{1 + e ^{- w^{T} x}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{1 + e ^{- w^{T} x}})

Treat

w, T

as constants

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{2 x}{sec ( x )})

\frac{d}{d x} (A e^{x} + B x e^{x})

x \to - 3 + lim (x + 1)

\int_{- 1}^{0.5} 1.5 x^{2} d x

\int \frac{x ^{3} - 4 x - 10}{x ^{3} - 3 x ^{2} - 4 x + 12} d x

What is (\partial)/(\partial x)(1/(1+e^{-w^Tx)}) ?
The answer to (\partial)/(\partial x)(1/(1+e^{-w^Tx)}) is (e^{-xw^T}w^T)/((1+e^{-xw^T))^2}