(** ** Definition and derivative of power function with natural number exponent *)
Definition pow_fct (n:nat) (y:R) : R := y ^ n.

Lemma derivable_pt_lim_pow_pos :
forall (x:R) (n:nat),
(0 < n)%nat -> derivable_pt_lim (fun y:R => y ^ n) x (INR n * x ^ pred n).