C1 smoothness of Liouville arcs in Arnol'd tongues

For the generic two parameter family of C-r circle diffeomorphisms of a general form we prove that the bifurcation arcs which correspond to Liouville irrational rotation numbers are C-1 smooth. As a consequence, we give an explicit formula for the derivative of all non-resonance arcs. Results of Arnol'd, Herman, and others give greater smoothness for a more restricted class of rotation numbers using KAM techniques.