proposition: Lemma ex_derive_mult (f g : R -> R) (x : R) : ex_derive f x -> ex_derive g x -> ex_derive (fun x : R => f x * g x) x.
proof: Proof. move => [d1 H1] [d2 H2]. exists (d1 * g x + f x * d2). now apply is_derive_mult. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv