<![CDATA[Understanding function derivatives shows global patterns of difficulty in comprehension and application. More research is needed to examine students' understanding of APOS theory. This research analyzes prospective mathematics teacher students' understanding of function derivatives based on mathematics anxiety. This study used a qualitative-exploratory design to describe the understanding of function derivatives of prospective mathematics teacher students with APOS theory, considering mathematics anxiety through assignments and interviews. A saturated sample of 26 students was studied. Instruments included math anxiety questionnaires, math ability tests, and function derivative tasks. Data was analyzed using triangulation, peer debriefing, member checking, data reduction, presentation, conclusion, and verification. The study of function derivatives, based on APOS Theory, integrates mental structures and mechanisms like encapsulation and coordination, showing proficiency in simple function derivatives and composition function derivatives but challenges with graphing function derivatives. This research emphasizes the need for teaching strategies that address math anxiety to improve conceptual understanding. It encourages further study of teaching interventions, emotional support, and the long-term impact of math anxiety.]]>
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