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))
]