I am reading the book http://neuralnetworksanddeeplearning.com/chap3.html by Michael Nielsen. So this is a question mostly for the people familiar with the book and understanding the material.
In the equations (71-75) we are trying to find a cost-function $C$ satisfying:
$$\frac{\partial{C}}{\partial{\omega_j}}=x_j (a-y),$$ $$\frac{\partial{C}}{\partial{b}}=(a-y),$$
where $w_j$ and $b$ are weights and bias of a neuron, $a$ is the output of the sigmoid function
$$a = \sigma(\sum{\omega_{j} x_j + b)}=\sigma(z).$$
We apply the chain rule (equation 73):
$$\frac{\partial{C}}{\partial{b}}=\frac{\partial{C}}{\partial{a}}\frac{\partial{a}}{\partial{b}}=\frac{\partial{C}}{\partial{a}}\sigma\prime(z).$$
And in the next line the author writes
Using $\sigma\prime(z)=\sigma(z)(1-\sigma(z))=a(1-a)$ the last equation becomes...
Where does this expression come from? $\sigma(z)(1-\sigma(z))$