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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int yz e^{y} + 2 y d y

x \to 0 lim (\frac{1 - cos ( 3 x )}{x})

\frac{d y}{d x}, 9 e^{x y} + 4 x^{2} - 2 y^{2} = 36

ln (\frac{4 x + 1}{x ^{2} - 2})

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

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