PART B$.$ Implementing Back Propagation

OK$,$ now it's time to implement back propagation. Complete the function back$\_$prop in the Network class to use a single training example to compute the derivatives of the loss function with respect to the weights and the biases. Remember, the pseudocode for back$-$prop was as follows:

Forward propagate the training example $x,y$

Compute the ${}^L=\frac{\text{d}\text{e}\text{l}\text{L}}{del{a}^L}o.g^{\text{'}}(z^L)$

For $l=L-1,$dots,$1$ :

$,\frac{\text{d}\text{e}\text{l}\text{L}}{del{W}^l}={}^{l+1}(a^l{)}^T$

$,\frac{\text{d}\text{e}\text{l}\text{L}}{del{b}^l}={}^{l+1}$

$,{}^l=(W^l{)}^T{}^{l+1}o.g^{\text{'}}(z^l)$

When you think you're done, instantiate a small Network and call back$-$prop for a single training example.