$[$BP $(20$ points$)]$ A neural network model is given as follows. $a$ is network output, $t$ is the ground$-$truth

label, and $L(a,t)$ is the network loss function.

a$.$ Derive the general formulation $($chain rule$)$ to compute the gradient of $L$ w$.$r$.$t$.$ to w$2.$

b$.$ If Mean Squared Error $($MSE$)$ is used as the loss function $L(a,t),$ drive the detailed gradient in

a$).$

c$.$ If Cross Entropy $($CE$)$ is used for the loss function $L(a,t),$ derive the detailed gradient in a$).$ I would prefer hand written clear solution