For Question $2$ to $4-$

Consider a simple output function $y=(w_1{x}_1+w_2{x}_2+b),$ where $$ is the sigmoid function and $x_1,x_2$ are the inputs. We wish to learn the weights $w_1,w_2,$ and

the bias $b.$ The loss function is defined as $L=(hat(y)-y{)}^3,$ where hat$(y)$ is the true label or $1).$ Take $x_1=1\mathrm{.}75,x_2=2\mathrm{.}5,y=0\mathrm{.}8,$ and hat$(y)=1.$

What is the value of del$\frac{L}{d}$ely $?$

What is the value of $delLdel{w}_1?$

Now, suppose that we have a $2x3$ matrix $M,$ and we use $2x2$ average pooling with stride $1$ to get $x=[x_1,x_2].$ What is del$\frac{L}{d}el{M}_{12}?$ is the element of $M$

in the $1$ st row and $2$nd column$).$ Assume $w_1=0\mathrm{.}5$ and $w_2=1.$