According to my teacher, for any two operators A and B, the commutators
[f(A),B]=[A,B]df(A)/dA
and [A,f(B)]=[A,B]df(B)/dB
He did not give any proof.
I can easily prove this for the particular cases
[f(x),p]=[x,p]df(x)/dx
and [x,pn]=[x,p]npn-1
But I don't see how the general formula is true. I...