Derivative of sigmoid

Question

I\'m creating a neural network using the backpropagation technique for learning.

I understand we need to find the derivative of the activation function used. I\'m using

Answer 1

A little algebra can simplify this so that you don't have to have df call f.
df = exp(-x)/(1+exp(-x))^2

derivation:

df = 1/(1+e^-x) * (1 - (1/(1+e^-x)))
df = 1/(1+e^-x) * (1+e^-x - 1)/(1+e^-x)
df = 1/(1+e^-x) * (e^-x)/(1+e^-x)
df = (e^-x)/(1+e^-x)^2