Derivative is one of the basic concepts of calculus, has an extremely rich practical background and wide application. However, "low exploration" of the limit thought in teaching and learning activities have caused difficulties in future advanced mathematics learning. The purpose of this study is to create a learning model that helps students understand calculus. The method in this research is using research and development method, designing a learning model using 6 questions cognitive model on derivative material. Based on the results of developing a new learning model in this study using the six questions cognitive model to explore mathematics from the six dimensions of "from where", "what ", "why", "how", "what if it changed" and "think about it", The teaching and learning activities when teaching derivative under the cultural background reflects the continuity, naturalness and order of teaching. The results of this study indicate that 6 question cognitive models can help students learn the basic concept of calculus. The results of this study can be implemented by teachers in schools to improve the quality of high school student learning