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##### Asked by: Zulmira Agin

science space and astronomy# How do you find the derivative of a sigmoid function?

Last Updated: 29th March, 2020

**derivative**of the

**sigmoid**is ddxσ(x)=σ(x)(1−σ(x)). Consider f(x)=1σ(x)=1+e−x.

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Herein, what is a derivative of a function?

The **derivative** measures the steepness of the graph of a **function** at some particular point on the graph. Thus, the **derivative** is a slope. The slope of a secant line (line connecting two points on a graph) approaches the **derivative** when the interval between the points shrinks down to zero.

Subsequently, question is, what is the use of sigmoid function? The main reason why we **use sigmoid function** is because it exists between (0 to 1). Therefore, it is especially **used** for models where we have to predict the probability as an output. Since probability of anything exists only between the range of 0 and 1, **sigmoid** is the right choice. The **function** is differentiable.

Herein, how do you find the derivative of a logistic function?

Differentiation of **logistic function**. The **logistic function** is g(x)=11+e−x, and it's **derivative** is g′(x)=(1−g(x))g(x). Now if the argument of my **logistic function** is say x+2x2+ab, with a,b being constants, and I derive with respect to x: (11+e−x+2x2+ab)′, is the **derivative** still (1−g(x))g(x)?

What is sigmoid derivative?

The **derivative** of the **sigmoid** is ddxσ(x)=σ(x)(1−σ(x)). Here's a detailed derivation: ddxσ(x)=ddx[11+e−x]=ddx(1+e−x)−1=−(1+e−x)−2(−e−x)=e−x(1+e−x)2=11+e−x ⋅e−x1+e−x=11+e−x ⋅(1+e−x)−11+e−x=11+e−x ⋅(1+e−x1+e−x−11+e−x)=11+e−x ⋅(1−11+e−x)=σ(x)⋅(1−σ(x))