The derivative is a central concept in calculus and has applications in many disciplines. This study explored students' understanding of derivatives with a particular focus on the graphical (geometric) representation. The participants were four Mathematics Honours students from a university in Lesotho. Data were generated from the written responses to five tasks and interviews, with all collection methods included. The Action-Process-Object-Schema (APOS) theory was used as the framework of analysis. The findings of the study show that the mental constructions that students developed in learning the derivative concept were mainly actions. The coordinated process conception of the derivative as the limit was evident with respect to algebraic representation but not in the graphical representation. Only one student showed that they had the process conception of the secant lines tending to the tangent line. It was also found that the process of tending to the limit operator was interpreted as "tending to" and "landing on" rather than "being in the neighbourhood of" by some students. These findings suggest that students should be made aware of the interpretation of "tending to" as implying "staying in" the neighbourhood rather than "landing on." Students should also be given activities based on derivatives that require translation from one mode of representation to another (algebraic to graphical in this case).