Kinda, yes. But also, specifically for calculus, thinking of things of the areas or slopes of other things, and how incremental changes affect them, is a very

Kinda, yes. But also, specifically for calculus, thinking of things of the areas or slopes of other things, and how incremental changes affect them, is a very simple and powerful lens for lots of things. Of course, lots of teachers just hammer the fiddly memorisables until the wonder is dead because they're easy to test and/or they don't have an intuitive feel of the underlying meaning themselves. And, for calculus, the fiddlies have never been so needless to know as everything non trivial is a computer job and no one is limiting things carefully to closed forms. Few people need the chain rule specifically, they'd be much better served with knowing that there's a thing called the chain rule and what that means, rather than the exact painful calculations and lists of forms.