proposition: Lemma Derive_mult (f g : R -> R) (x : R) : ex_derive f x -> ex_derive g x -> Derive (fun x => f x * g x) x = Derive f x * g x + f x * Derive g x.
proof: Proof. move => H1 H2. apply is_derive_unique. now apply is_derive_mult ; apply Derive_correct. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv