Consider the problem of classifyingD dimensional inputs xRD. Suppose we have 2 classes and the output is denoted y{0,1}. If we use a binary logistic regression classifier then the model is:

pb(yx)=Binomial(y(wTx+b))

where(a)=1+ea1 and wRD,bR, are the parameters of the model.

The derivative of the sigmoid function has a special form which can be useful in computing gradients. Show that dad=(1). Use this fact to derive the form of d2ad2.