Product rule
The product rule can be written with differential operators as
D(xψ) = (D(x))ψ + xD(ψ)
Example 1
We'll convert this to
D(xψ) – xD(ψ) = (D(x))ψ
and because D(x) = 1 we get
D(xψ) – xD(ψ) = 1ψ
Differential operators can be treated as ordinary numbers
(Dx – xD)ψ = 1ψ
so that
Dx – xD = 1