I hate the notation for derivatives that looks like a fraction, like this. The whole point of notation is to convey meaning clearly and avoid confusion.
Notation like f’(x) or derivative(f(x),x) works just as well and doesn’t look like a fraction. Looking like a fraction is especially problematic when you’re actually encouraged to do some things that seem to require that it is really a fraction, or suggest that it is really a fraction, or at least cloud the issue.
After all, most of the people who use calculus are the students studying it.
In fact, to the inevitable comments that say it can be written this way and the result works, I would like to make an example of the FORTH programming language, some versions of which let you give variables and subroutines names like 3 or |ll|l|| (a string of lowercase Ls and pipe characters). Creating a subroutine that returns 5 and naming it 3 lets you add 3 and 4 and get 9, for example. It can be written this way and the result works. Now, the point here is to comment on a notation as a notation - why in the world is this a good notation?