Consider the logistic regression classifier applied to a sample $x($bias feature added$)$ with correct label $y$ using weights vector $w($bias

corrected$).$ The forward propagation for calculating the sample's loss is:

$z=w^T$xlongrightarrowa$=(z)longrightarrowL=-log(a^y(1-a{)}^{1-y}).$

Calculate the gradient of the loss using the chain rule $gra{d}_w(L)=gra{d}_w(z)gra{d}_z(a)gra{d}_a(L)$ and express it in terms of $x,a,$ and $y.$