
theorem
for R being domRing
for p being Element of the carrier of Polynom-Ring R
for n being non zero Element of NAT
holds (Deriv R).(p|^n) = n * ((p|^(n-1)) * (Deriv R).p)
proof
let R be domRing, p be Element of the carrier of Polynom-Ring R;
let n being non zero Element of NAT;
reconsider n1 = n - 1 as Nat;
(Deriv R).(p|^(n1+1)) = (n1 + 1) * ((p|^n1) * (Deriv R).p) by RINGDER1:7;
hence thesis;
end;
