Homework Statement
A and B commute with their commutator, C=[A,B]
Show that [A, F(B)] = [A, B]F'(B)
F(B) = ∑n=0∞fnBn
Homework Equations
[A,B] = AB - BA
[A,BC] = [A,B]C + B[A,C]The Attempt at a Solution
So all I can think to do is:
[A,Bn] = [A,BBn-1] = [A,B]Bn-1 + B[A,Bn-1]...