It’s funny, with the increase in use of numerical models, so much math has been turned into computer code. Derivatives and integrals as well are defined by finite difference formulas that serve as the basis for the notations. The point of them isn’t to explain, it’s just to simplify writing and reading it. I agree it can be a bit obtuse but if you had to write out a for loop to solve a math equation every time it would take forever lol