The purpose of this research is to investigate high school mathematics teachers’ pedagogical content knowledge in the context of subject matter knowledge on the definition of derivative, the visualization of the definition of derivative, and the relationship between derivative and continuity. The subject matter knowledges of teachers are examined in the form of defining derivatives and giving examples to derivatives from everyday life, visualizing the definition of derivatives and explaining the relationship between derivatives and continuity. The case study design of the qualitative research models is used in this research. The research is carried out in a city of the Black Sea Region of Turkey during the fall semester of 2015-2016 academic terms. The participants of the research are four mathematics teachers two graduated from the faculty of science-letters and the other two graduated from the faculty of education. The data collection tool is a semi-structural interview protocol developed by the researchers. The research data are analyzed by content analysis. According to the results of the research, high school mathematics teachers made necessary but insufficient definitions for the definition of the derivative. The teachers have presented prototype examples such as instant change, rate of change and exchange ratio in relation to the derivative. Two of the teachers were found to have made sufficient explanations for the relationship between the derivative and continuity while the other two explained necessary but inadequately manner for the same relationship.