True. Knuth had a paper where he suggests using (a slightly modified) O notation for teaching calculus.

https://www-cs-faculty.stanford.edu/~knuth/calc

From the Arxiv paper:

Students have to memorize a diversity of processes for essentially performing the same task.

Is that true for differentiation ? I don't recall having to memorize many things, just how differentiation composes over +,-,×,÷, function composition and the differential of a few standard forms.

Symbolic integration, on the other hand, is a whole can of worms.