Math Help: Commutator & Relation [f(\hat{A}),\hat{B}]

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Does the relation $[f(\hat{A}),\hat{B}] = df(\hat{A})/d\hat{A}$ follow when A commutes with [A,B]? or is this only valid when [A,B]=1?

 

[StatusX]

If A commutes with [A,B] then:

$$[f(A),B] = [A,B] f'(A)$$

You should try to derive this formula. Use a taylor expansion of f(A), ie:

$$f(A) = f(0) + f'(0) A + \frac{1}{2} f''(0) A^2 + ...$$