The tree model of a meromorphic plane curve

We associate with a plane meromorphic curve f a tree model T(f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobien J(f,g)) in terms of T(f) (resp. T(fg)). We also characterize the regularity of f in terms of its tree and we give a bound for the number of its irregular values.