proposition: Lemma is_derive_div : forall (f g : R -> R) (x : R) (df dg : R), is_derive f x df -> is_derive g x dg -> g x <> 0 -> is_derive (fun t : R => f t / g t) x ((df * g x - f x * dg) / (g x ^ 2)).
proof: Proof. intros f g x df dg Df Dg Zgx. evar_last. apply is_derive_mult. exact Df. apply is_derive_inv with (2 := Zgx). exact Dg. simpl. now field. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv