Assume the following ANN with a single neuron.

Calculate the outputs for the inputs $x(1)=(x_1,x_2)=(0\mathrm{.}6,2\mathrm{.}1)$ and $x(2)=(x_1,x_2)=(2,1),$

where $(w_0,w_1,w_2)=(-1\mathrm{.}5,0\mathrm{.}5,1)$ and the activation function is sigmoid $(s)=\frac{1}{1+e^{-s}}.$

Calculate the MSE loss function.

If the real outputs $($ground truth$)$ at these data points are $y(1)=2,y(2)=-1,$ calculate the $\frac{\text{d}\text{e}\text{l}\text{J}}{\text{d}\text{e}\text{l}\text{w}2},$

where $J$ is the mean squared error.