Final expressions for the biases of the hidden layer

For the sake of completeness, we list the derivatives of the biases, which are

$$ \frac{\partial C}{\partial b_{1}^{(1)}}=\delta_1^{(1)}, $$

and

$$ \frac{\partial C}{\partial b_{2}^{(1)}}=\delta_2^{(1)}. $$

As we will see below, these expressions can be generalized in a more compact form.