The derivative is not only an important subject for mathematics but also is an important subject for engineering, physics, economy, chemistry, and statistics. Especially, mathematics depends on strongly preceding learning and the subject of derivative will be used in university education by all students. Therefore, it is one of the most important subjects. This study's purpose is to explore student mistakes and errors in derivative and determine the areas in which students have probable misconceptions. For this purpose, 7 questions were chosen from "the Student Placement Test" (OSS). These questions were transferred into open-ended questions. The results of the study, which took place at sixth form college, are described and discussed. The test was administered to 53 students from Balikesir Fatma Emin Kutvar Anatolian High School in the fall-term of 2005-2006. Determining the possible misconceptions should help teachers when they teach this subject. The study findings showed that students could not understand derivative definition that depends on limit, make mistakes in composite functions and trigonometric functions, and establish wrong relations between tangent's slope, and normal's slope. Teachers need to be able to find errors and misconceptions in students' solutions. Teachers also need to be applying meaningful learning strategies such as concept maps, worksheets about derivative (e.g. Appendix B, Appendix C).