@ramsay "Like, you shouldn't feel bad about thinking of these things as infinitesimals. That's the idea. But the reason people say not to think of dy/dx as a fraction is twofold. 1) Mathematically, that's not literally what it is. It's a limit etc etc. 2) Sometimes, if you are too uncareful with treating these terms as variables, you can come to a result that's just actually wrong. I don't have an example off the top of my head, but when I was teaching calculus, I saw this happen now and then.
On the other hand, I don't have a problem with people reading this as "infinitesimal change of y o…