proposition: Lemma ex_derive_pow (f : R -> R) (n : nat) (x : R) : ex_derive f x -> ex_derive (fun x : R => (f x)^n) x.
proof: Proof. case => l H. exists (INR n * l * (f x)^(pred n)). by apply is_derive_pow. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lim_seq Iter Hierarchy Continuity Equiv