This qualitative exploratory case study delves into learners' understanding of differentiation through the first principle and power rule. The study adopted the action, process, object, and schema (APOS) theory as a lens to track learners' understanding of these concepts using the activities, classroom discussion, and exercise (ACE) teaching cycle. The findings of the study highlight learners' algebraic conceptual obstacles in comprehending the first principle and power rule. Moreover, the study demonstrates the effectiveness of the ACE teaching cycle as a valuable tool for unveiling learners' conceptual obstacles. Overall, this research contributes to the advancement of knowledge and practice in mathematics learning by identifying critical issues, emphasising the significance of algebraic skills in differentiation, and showcasing the value of the ACE teaching cycle in supporting learners' understanding. As a result, the study suggests the need for further research to enhance learners' algebraic skills, which are essential for successful differentiation.