proposition: Lemma is_derive_n_inv n x : x <> 0 -> is_derive_n Rinv n x (\big[Rmult/1%R]_(i < n) - INR (1 + i) * / x ^ (1 + n))%R.
proof: Proof. move=> Hx. have := is_derive_n_powerRZ (-1) n x (or_intror Hx). apply: is_derive_n_ext. by move=> t; rewrite /= Rmult_1_r. Qed.
imports: Coq(Reals Psatz) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Stdlib MathComp