sigmoid函数求导过程

sigmoid函数如下：

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

对其求导过程：

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