The

sigmoid function is

f(x) = 1
---------
-Bx
1 + e

when e is the

exponential function and B is a parameter to adjust the steepness.

This function has the following properties:

One practical application of this function is the firing function in multi-layer perceptron neural networks.

It is used because of its simple derivative:

f'(x) = -Bx
B e
--------------
-Bx 2
( 1 + e )
= B f(x) (1 - f(x))