The aim of this study was determined as stating Mathematics candidate teachers' understanding of derivative concept and difficulties they encounter within the process of understanding the concept. Accordingly this study concerned relations between derivative and limit, derivative and rate of change while describing Mathematics candidate teachers' understanding of derivative concept. The research is a case-study. The working group was composed of 45 candidate teachers registered to Mathematics Education program in a state-owned university. The data of the study were gathered with: 2 written exams applied with a week in between and clinical interviews conducted with 6 candidate teachers. In order to state opinions directing candidate teachers to right answers and wrong answers, the data coming from clinical interviews were categorized based on their similarities. The study conducted showed that candidate teachers have superficial knowledge about derivative concept. Since candidate teachers, whose understandings were mainly restricted to definitions, they could not fully consolidate the content of definitions. As another piece of finding, the research came up with that candidate teachers were more successful the interpretation of derivate concept in algebraic form rather than graphical and table representations.