(15 points) We consider logistic regression for a 2-class classification setting. Let X= {(xi,yi),,(xn,yn)} be a dataset for 2-class classification, where xiRd and yi{0,1}. For any aR, let (a)=1+exp(a)1. For each sample (xi,yi)Rd{0,1}, the conditional log-likelihood of logistic regression is L(yixi,w)=yilog((wxi))+(1yi)log((wxi)). Derive the gradient of L(yixi,w) with respect to wj (the j-th coordinate of w), i.e., wjL(yixi,w). (You must clearly mention the derivative properties used.)