In fact, checking the composition law is sufficient. See the attached image taken from P. M. Cohn, "Lie groups". ("Analytic" means that it can be expressed locally as a power series). So, it is more than just "differentiable". But usually, in applications, we are dealing with elementary functions that are analytic in this sense. Problems would arise with functions like "absolute value" which is not differentiable at 0.
