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

The derivative of 1/(1+e^{-wx}) is (e^{-wx}w)/((1+e^{-wx))^2}

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

The first derivative of 1/(1+e^{-wx}) is (e^{-wx}w)/((1+e^{-wx))^2}

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

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

Solution steps

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

Treat

w

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - \frac{2 cos ( x )}{sin ( x )} d x

x \to 5 + lim (\frac{6}{x - 5})

x \to 0 lim (x^{3} cos (\frac{6}{x}))

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

\int 3 x^{\frac{1}{2}} d x

What is the derivative of 1/(1+e^{-wx}) ?
The derivative of 1/(1+e^{-wx}) is (e^{-wx}w)/((1+e^{-wx))^2}
What is the first derivative of 1/(1+e^{-wx}) ?
The first derivative of 1/(1+e^{-wx}) is (e^{-wx}w)/((1+e^{-wx))^2}