Problem $7\mathrm{.}1$ A two$-$layer network with two hidden units in each layer can be defined as:

$y={}_O+{}_{1}a[{}_{O1}+{}_{11}a[{}_{O1}+{}_{11}x]+{}_{21}a[{}_{O2}+{}_{12}x]]$

$+{}_{2}a[{}_{O2}+{}_{12}a[{}_{O1}+{}_{11}x]+{}_{22}a[{}_{O2}+{}_{12}x]]$

where the functions $a[*]$ are ReLU functions. Compute the derivatives of the output $y$ with respect to

each of the $13$ parameters $.,{}_{..,}$and $..$ directly $($i$.$e$.,$ not using the backpropagation algorithm$).$ The

derivative of the ReLU function with respect to its input dela$\frac{z}{d}$elz is the indicator function $],$

which returns one if the argument is greater than zero and zero otherwise $($figure $7\mathrm{.}6).$