On the n -th Derivative of a Determinant of the j -th Order
John G. Christiano, James E. Hall · Mathematics Magazine · 1964
We interpret Afo as the identity operator on f. The operator Afn acts only on the function f, so that (uv)A,= (u,An)v and (uv)Al =u(vA'). No meaning need be attached to vA' since we shall never apply A' to a function not containing u as a factor. Note that (uv) (Au +A,) = (uv)Au + (uv)A, and that AuAV = A,Au trivially, because Af operates specifically on the function f. Using equation (2), we can write equation (1) as