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

Lemma Derive_n_pow i p x:
Derive_n (fun x : R => x ^ p) i x =
match (le_dec i p) with
| left _ => INR (fact p) / INR (fact (p -i)%nat) * x ^ (p - i)%nat
| right _ => 0
end.