(** * Definitions on [R] *)

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

Lemma Derive_div (f g : R -> R) (x : R) : ex_derive f x -> ex_derive g x -> g x <> 0 -> Derive (fun y => f y / g y) x = (Derive f x * g x - f x * Derive g x) / (g x) ^ 2.