The operator identity [ a , b c ] = a b c − − b c a = a b c − − b a c + b a c − − b c a = [ a , b ] c + b [ a , c ] allows the evaluation of the commutator of P with any power of X, and it implies that [ P , X n ] = − − i n X n − − 1 which, together with linearity, implies that a P -commutator effectively differentiates any analytic matrix function of X.