Section is_derive_mult.
Context {K : AbsRing}.
End is_derive_mult.

Lemma Derive_n_pow_smalli: forall i p x, (i <= p)%nat ->
Derive_n (fun x : R => x ^ p) i x
= INR (fact p) / INR (fact (p - i)%nat) * x ^ (p - i)%nat.