I'm new to NN. I am trying to understand some of its foundations. One question that I have is: why the derivative of an activation function is important (not the function itself), and why it's the derivative which is tied to how the network performs learning?

For instance, when we say a constant derivative isn't good for learning, what is the intuition behind that? Is the activation function somehow like a hash function that needs to well differentiate small variance in inputs?