From the Pythagorean Theorem to the definition of the derivative function

In this paper, the authors describe some activities which might be implemented within the framework of Slovak and Polish GeoGebra Institute. It's presented new goals defined in new Slovak curriculum ISCED 3 for Mathematics at secondary schools. Several students' works, which use the GeoGebra software, become a concrete example for motivation during the educational process. GeoGebra can help teachers to use the time more effectively. The authors present introduction method of the definition of the derivative function through the Pythagorean Theorem.