Archimedean t-norms in the unit interval \([0,1]\) admit a representation of the form \(T(x,y)=t^{[-1]}(t(x)+t(y))\) where \(t\) is an additive generator (and a multiplicative version is also possible). The problem of finding explicit expressions for \(t(x)\) given \(T\) has received a lot of attention in the literature without assuming derivability conditions. The use of partial derivatives of \(T\) to determine \(t\) was initiated many years ago by \textit{M. S. Tomás} [Stochastica 11, No. 1, 25--34 (1987; Zbl 0658.39007)]. The authors of this paper present some results to be applied for t-norms with partial derivatives, and techniques are illustrated with well-known examples of such t-norms. Geometrical considerations about t-norms and their generators are given.