Here I'll post derivatives through definition of limits of delta-x (or differential of x, but let's say that you're a Calculus 1 student who doesn't have to know what the hell that means), and not through rules or theorems of derivation. I'll try to post those which are interesting to me or hard ones, kinda like the ones which almost everybody would use rules of derivation 'cause why the hell would you try to derive a trigonometric-exponential funcion with a limit lol.