sigmod函数求导

sigmod函数：

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

求导：

\[\frac{\partial f(z)}{\partial z}=\frac{-1*-1*e^{-z}}{(1+e^{-z})^2}
=\frac{e^{-z}}{(1+e^{-z})^2}
=\frac{1+e^{-z}-1}{(1+e^{-z})^2}
=\frac{1}{1+e^{-z}}-\frac{1}{(1+e^{-z})^2}
=\frac{1}{1+e^{-z}}(1-\frac{1}{1+e^{-z}})
\]

\[=f(z)(1-f(z))
\]