Derivation of partial derivatives for isothermal multi-component mixtures needed for development of universal models for multi-phase multi-component flows is presented. The equations of state and the derivative approximations as functions of temperature and pressure for the elementary mixture constituents are assumed to be known. The so called universal fluid is introduced consisting of an arbitrary number of miscible and non-miscible components. This fluid model describes in its limiting cases gas, or gas mixture, or liquid, or solution of liquids, or gas-liquid solutions with an arbitrary number of gaseous and liquid components, or gas-liquid solutions containing immiscible liquid or solid particles. In addition, one component liquid-gas and solid-liquid equilibrium mixtures are considered.