Action-Process-Object-Schema (APOS) is used to study students' understanding of the relationship between tangent planes and the differential. An initial conjecture, called a genetic decomposition, of mental constructions students may use in constructing their knowledge of planes, tangent planes, and the differential is proposed. It is tested with semi-structured interviews with 26 students. Results of the study suggest that students tend not to relate these ideas on their own and suggest ways to refine the initial genetic decomposition in order to help students to better understand these concepts.