Any apoptotic process in a dendritic cell, a cell of hematopoietic origin, typically resident in particular tissues, specialized in the uptake, processing, and transport of antigens to lymph nodes for the purpose of stimulating an immune response via T cell activation. [ GOC:BHF http://purl.obolibrary.org/obo/CL_0000451 GOC:mtg_apoptosis http://www.ncbi.nlm.nih.gov/pubmed/15059845 ]