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The well known formula $[X,Y]=\frac{1}{2}\frac{{\partial }^2}{\partial t^2}{|}_0{(}_{-t}^Y{ø}_{-t}^X{ø}_t^Y{ø}_t^X)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.