proposition: 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)).
proof: Proof. move => H. apply is_derive_unique. apply is_derive_pow. by apply Derive_correct. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv