A simple and explicit mnemonic procedure for the derivation of the set of Maxwell`s first order partial derivatives and the Clausius relationships, in terms of fundamental thermodynamic parameters (V, T, P and S), is described with illustrative examples. The procedure has been applied, in the first instance, to thermodynamic system of constant and variable composition and, later, extended to cover cases of constant volume, temperature, pressure and entropy. All this has been taken up with the aid of a computational procedure based on an instructive loaic rather than on a mathematical operational logic.