In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative software product, and considering the possibility of using a public-domain software such as MAXIMA. Here we make a comparative study of DERIVE and MAXIMA as support tools for a Calculus course for first year Engineering students. First we have a brief look at the use of both systems in Spain and our experience with them. Then, we make a comparative study of DERIVE and MAXIMA, following a specific protocol based on a Systemic Model of Software Quality. Finally, we perform a quantitative evaluation and we conclude that MAXIMA can be used to carry out learning activities similar to those that we have been doing with DERIVE. (Contains 6 figures and 3 tables.)