Sigmoid関数の導関数

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y(z) = 1 / (1 + exp(-z))　＜－シグモイド関数

y(z)’ = y(z)・(1 – y(z))　＜－これを求めたい

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u = 1 + exp(-z)

t = -z

dy(z)/dz = dy(z)/du ・du/dt ・dt/dz

y(z) = 1/u

dy(z)/du = – 1/u^2

du/dt =  exp(t)

dt/dz = -1

dy(z)/dz = exp(-z)/( 1 + exp(-z))^2

= 1/( 1 + exp(-z)) ・(1 +  exp(-z) – 1 )/( 1 + exp(-z)) 

= 1/( 1 + exp(-z)) ・(1 – 1/( 1 + exp(-z)))

= y(z) ・(1 – y(z))

以上