(** * Definitions on [R] *)

Definition Derive (f : R -> R) (x : R) := real (Lim (fun h => (f (x+h) - f x)/h) 0).

Lemma Derive_pow (f : R -> R) (n : nat) (x : R) : ex_derive f x -> Derive (fun x => (f x)^n) x = (INR n * Derive f x * (f x)^(pred n)).