(Neural Network) Derivative of sigmoid function

Process:

$$ f(z)=\frac{1}{1+e^{-z}}$$
$$ f'(z)=\frac{e^{-z}}{{(1+e^{-z}})^{2}}$$
$$ =\frac{1+e^{-z}-1}{{(1+e^{-z}})^{2}}$$
$$ =\frac{1}{(1+e^{-z}}) – \frac{1}{{(1+e^{-z}})^{2}}$$
$$ =y(1 – y)$$