What is the derivative of sigmoid function: NSK PSK\sigma(x) = \frac{1}{1+ e^{-x}}ZSK

Madeline Lott

Madeline Lott

Answered question

2021-12-11

What is the derivative of sigmoid function:
σ(x)=11+ex

Answer & Explanation

Mary Herrera

Mary Herrera

Beginner2021-12-12Added 37 answers

The derivate is:
ddxσ(x)=σ(x)(1σ(x))
Then,
ddxσ(x)=ddx[11+ex] =
= ddx(1+ex)1=
= (1+ex)2(ex)=
=ex(1+ex)2=
=11+ex×ex1+ex=
=11+ex×(1+ex)11+ex=
=11+ex×(1+ex1+ex11+ex)=
=11+ex×(111+ex)=
=σ(x)×(1σ(x))

eninsala06

eninsala06

Beginner2021-12-13Added 37 answers

f(x)=1σ(x)=1+ex
f(x)=ddx(1σ(x))=σ(x)σ(x)2,
Thus,
f(x)=ddx(1+ex)=ex=1f(x)=11σ(x)=σ(x)1σ(x).

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