We often thing that math is a bunch of rules and we can only do the math that the rules dictate. But it develops the other way around. There is some kind of math that we want to be able to do, and we just need to create rules that allow us to do that math.
Newton wanted to do a specific kind of math related to physics where he needed to divide things into infinitely small chunks. You can’t just do that without well thought out rules without it going crazy and incomprehensible. So the rules to do that were not fully developed around that time (though, there was already a lot of work done on Calculus before Newton), and so Newton just found out the rules needed to do what he wanted to do.
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