Central-commutator differentiation rule
= Central-commutator differentiation rule
If $D=[A,B]$ commutes with $A$, then $[A^n,B]=nDA^{n-1}$. A convergent <power series> therefore gives $[F(A),B]=DF'(A)$ on a common domain where termwise operations are justified. For unbounded <linear operators>, the domain condition is essential.