It is also easy to see that our previous equation can be written as
$$ \delta_j^L =\frac{\partial {\cal C}}{\partial z_j^L}= \frac{\partial {\cal C}}{\partial a_j^L}\frac{\partial a_j^L}{\partial z_j^L}, $$which can also be interpreted as the partial derivative of the cost function with respect to the biases \( b_j^L \), namely
$$ \delta_j^L = \frac{\partial {\cal C}}{\partial b_j^L}\frac{\partial b_j^L}{\partial z_j^L}=\frac{\partial {\cal C}}{\partial b_j^L}, $$That is, the error \( \delta_j^L \) is exactly equal to the rate of change of the cost function as a function of the bias.