Various studies have concluded that many students have difficulty understanding concepts related to function derivatives. One of the concepts in function derivatives is higher-order derivatives, primarily the nth derivative pattern. This study aims to: (1) identify various types of learning obstacles experienced by prospective mathematics teacher students on high-level derivative topics; (2) design alternative didactic designs based on the findings of learning obstacles; and (3) identify the effectiveness of the didactic design developed for the learning obstacle solution. This study used a qualitative method with a Didactic Design Research (DDR). Involves 41 students who have received Differential Calculus courses and 43 second-semester students at one of the universities in Indonesia. Data from test results, interviews, and document studies were analyzed through identification, clarification, reduction, and verification techniques and presented narratively. The results showed that: (1) students were still experiencing epistemological, didactical, and ontological types of conceptual and instrumental learning obstacles; (2) the development of a didactic design based on learning obstacle findings refers to the Theory of Didactical Situation combined with the Socratic Questioning technique; and (3) the alternative didactic design is quite effective in overcoming the initial learning obstacle, but a new obstacle appears, namely the ontological psychological type obstacle. The results of this study indicate that the phenomenon of learning obstacle findings and the developed didactic design can be used to improve the quality of learning on an ongoing basis.