(** Definition of ps_atan's derivative *)

Definition Datan_seq := fun (x : R) (n : nat) => x ^ (2*n).

Lemma Datan_is_datan : forall (N : nat) (x : R), -1 <= x -> x < 1 -> derivable_pt_lim (fun x => sum_f_R0 (tg_alt (Ratan_seq x)) N) x (sum_f_R0 (tg_alt (Datan_seq x)) N).