What's the purpose of the “o(1-o)” in the back propagation algorithm

I'm not sure what the purpose of the o(1-o) in the back propagation algorithm achieves? I'm guessing it's related to using the sigmoid function on the output but I'd like to have a proper understanding of the math behind it. Thanks!

• What research have you done? Back propagation is covered well in many textbooks. Have you tried reading them? We expect you to do a significant amount of research on your own before asking. – D.W. Mar 2 '14 at 15:39

Along the way of calculating the gradient, you have to find the derivative of the activation function. When you take the most common activation function, i.e. the logistic rule or sigmoid function $o(z) = \frac{1}{1 - e^{-z}}$ and you differentiate it with respect to the neurons' input $z$ then you get $do/dz = o(1 - o)$. Hence, you are correct, this is related to the use of the sigmoid function, and figuring out in which direction the gradient points.