Analyzing the last results

This is an important expression. The second term on the right handside measures how fast the cost function is changing as a function of the $j$th output activation. If, for example, the cost function doesn't depend much on a particular output node $j$, then $\delta_j^L$ will be small, which is what we would expect. The first term on the right, measures how fast the activation function $f$ is changing at a given activation value $z_j^L$.

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