1. (a) The logistic sigmoid function is defined as 1 f(z) 1+ exp(-az) where a > 0. Show that the derivative of the sigmoid function is df(z) dz = = aƒ(z) [1 − f(z)] . (b) The hyperbolic tangent function is defined as f(z)= a tanh " where cand a are controlling parameters. Show that the derivative of the hyperbolic tangent function is df(z) с dz = 2a [a² – f²(z)].

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