$3.$ Neural networks $(10$ points$).$ Consider a simple two$-$layer network in the lecture slides. Given n training data $($x$,$ y$\text{'}),$ i $=1,...,$ n$,$ the cost function used to training the neural networks $$ l$($w$,$a$,$B$)=($y $($WTz:$))?$ a $=$ i$=1=$ where o$($x$)=1/(1+$e$-2)$ is the sigmoid function, zi is a two$-$dimensional vector such that $=$ g$($a$+$c$),$ and $==$ g$(812).($a$)(5$ points$)$ Show the that the gradient is given by n al$($w$,$a$,)$w $=2($x $$ g$($x$))($u$)(1$ F$($x$))=,$ i$=1=$ where ui $=$ wTzi. $($b$)(5$ points$)$ Also show the gradient of l$($w$,$a$,)$ with respect to a and B and write down their expression.