Suppose that A is an algebra with unit 1 and a is an element of A which is not algebraic (i.e. {1,a,a², ¼} isn't a linearly independent set). Let B be the subalgebra of A generated by 1 and a. Define a mapping D of B into B by D(l₀ + l₁a + ¼+ l_naⁿ) = l₁ + 2l₂a + ¼+ nl_na^n-1. Obviously D is a derivation on B and isn't inner, since B is commutative and D ¹ 0.