This study aims to describe students' discovery abilities in the learning process and when facing problems in the material derived from algebraic functions. The research was carried out in one of the Senior high schools in Gorontalo. This research is a type of qualitative descriptive research. The subjects of this study were students of class XI who opened 318 people. The techniques used in data collection are initial tests, interviews, documentation, and observation. Data analysis techniques in this study are data reduction, data presentation and conclusions. The results showed that students' discovery abilities on the derivative material of algebraic functions varied. Some have high abilities, medium abilities, and low abilities, but in general, they are dominated by students who have moderate abilities.