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This paper presents the mathematical design of a small part of a reference epistemological model which, once concluded, should support the educational organization of a study process comprising: the development of the functional modelling with parameters, elementary differential calculus raison d'être in high school, and the first developments of calculus in several variables at university. Hereto we focus in the moment in which we already hold the derivative as a work tool to show the progressive development, and the relative completion of mathematical praxeologies that are built as progress gains ground in the different levels of functional modelling. This proposal is submitted from an Anthropological Theory of the Didactic scope and represents a small contribution to the didactic purpose of placing the mathematical modelling as an instrument that allows to articulate and give meaning to school mathematics. [ABSTRACT FROM AUTHOR]