Deriving N=2 S-dualities from scaling for product gauge groups

S-dualities in scale invariant N=2 supersymmetric field theories with product gauge groups are derived by embedding those theories in asymptotically free theories with higher rank gauge groups. S-duality transformations on the couplings of the scale invariant theory follow from the geometry of the embedding of the scale invariant theory in the Coulomb branch of the asymptotically free theory.