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

Lemma filterdiff_pow_n {K : AbsRing} (x : K) (n : nat) :
(forall a b : K, mult a b = mult b a)
-> filterdiff (fun y : K => pow_n y n) (locally x)
(fun y : K => scal y (mult (nat_to_ring n) (pow_n x (pred n)))).