1. The problem statement, all variables and given/known data Analytic functions of operators (matrices) A are defined via their Taylor expansion about A=0 .Consider the function g(x) = exp(xA)Bexp(-xA) Compute : dng(x) /dxn |x=0 for integer n and then show that :exp(A)Bexp(-A)= B+[A,B] +1/2 [A,[A,B]] +1/6[A,[A,[A,B]]]+ ... 2. Relevant equations for the first part of the question i don't understand what x=0 means in the formalism and it is unclear how one should proceed ,becuase we are dealing with operators. about the second part i would like to note that : g(1) =g(0) +g'(0) +1/2 g''(0)+ ... if A=0 e^0 =1 and we start with B in the expansion formula 3. The attempt at a solution About the first part i cannot imagine how i could proceed ,but about the second question i think we must use somehow a taylor expansion to resemble the monsterous expression of the RHS. But what i can't see is how one should manipulate [A,B], how could this come from a taylor expansion of the exponential ?