Final answer:
The primary germ layer responsible for the differentiation of both nervous tissue and the epidermis is the ectoderm, which during development gives rise to various cell types including neuronal and epithelial cells.
Step-by-step explanation:
The nervous tissue and the epidermis of the skin are derived from the primary germ layer called the ectoderm. During the process of gastrulation, three primary germ layers form: the ectoderm, the mesoderm, and the endoderm. The ectoderm specifically gives rise to the nervous system and the epidermal skin cells. This layer undergoes a transformative process where signaling molecules direct the differentiation of cells into either the nervous system or the epidermal cells that form the skin.
In vertebrates, the ectoderm forms both neuronal tissues comprising the central and peripheral nervous systems and epithelial cells including those that make up the epidermis. The intricate development of these two systems from the same primary germ layer exemplifies the precise regulatory mechanisms that govern embryogenesis and organogenesis, the process of organ formation.