> I would also have a hard time processing/registering something if I'm not able to derive it analytically from first principles.

This really resonates with me. I always had a really hard time with anything where I just had to memorize formulas, but I didn't have any issues if I could derive it myself. For this reason I actually struggled a lot more with algebra in HS than I did with calculus in college. I don't know if it's just the teachers I had growing up or if it's a more broad issue with how the curriculum is structured, but I didn't even realize you could derive things from first principles until I took calculus in college.