Problem $2($Practice of vector$-$based backpropagation$).$ You are required to calculate the gradients of $f(x,w)=||(Wx)|{|}^2$ with respect to $x_i$ and $W_{i,j}.$ Here $||*|{|}^2$ is the calculation of L$2$ loss, $W$ is $3-$by$-3$ matrix and $x$ is $3-$by$-1$ vector, and $(*)$ is sigmoid function that performs element$-$wise sigmoid operation.

Use computational graph for calculation

Note: You are free to choose the inputs of your computational graph.