Process:

$$ f(z)=\frac{1}{1+e^{-z}}$$

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

$$ =\frac{1+e^{-z}-1}{{(1+e^{-z}})^{2}}$$

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

$$ =y(1 – y)$$

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# (Neural Network) Derivative of sigmoid function

SY -> CS -> LA -> SEA

Process:

$$ f(z)=\frac{1}{1+e^{-z}}$$

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

$$ =\frac{1+e^{-z}-1}{{(1+e^{-z}})^{2}}$$

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

$$ =y(1 – y)$$