Honestly, for the first year or two after learning about it (which is the only time where it’s really relevant) that’s exactly what I did. Spend 30 seconds, derive something that’s definitely correct, and never worry again about your memory randomly failing you

That depends on how often you use it. If I needed to write quicksort as often as the quadratic formula, I’d probably remember it. And if I only used the quadratic formula as often as I do quicksort, I’d just derive it each time.