Compare https://twitter.com/mrkgnaow/status/876007524968800256 to Haskell, should probably stress this before each talk
This is a list of different ways of thinking about or conceiving of the derivative, rather than a list of different logical definitions. Unless great efforts are made to maintain the tone and flavor of the original human insight, the differences start to evaporate as soon as the mental concepts are translated into precise, formal and explicit definitions.
I can remember absorbing each of those concepts as something new and interesting, and spending a good deal of mental time and effort digesting and practicing with each, reconciling it with the others. I also remember coming back to revisit these different concepts later with added meaning and understanding.