This study is about an analysis of the effects that the incorporation of cutting-edge technology produces in the teaching field of the elementary theory of mathematical analysis. Specifically, the case of the relations between fand f', i.e. between a function and its derivative or the function and its primitives. For this, we use an experimental design which intentionally and systematically incorporates the calculators with graphical capacity. Far from assuming as a theoretical priori that such incorporation would have significant educational advantages, we approach the examination of the learning nature as an investigation matter in that technological area. In such sense, the study we are reporting now, allows to take a rational and critical attitude towards the existence of technological resources designed with teaching purposes.