An electric vehicle transmission (7) has a drive input shaft (10), a drive output shaft (11), a first planetary gearset (P1), a second planetary gearset (P2), and a third planetary gearset (P3). The drive input shaft (10) is designed to be coupled to an electric machine (6). In addition, at least functionally a first shifting element (A), a second shifting element (B), a third shifting element (C), and a fourth shifting element (D) are provided. Also disclosed is a drive system (4), a vehicle drive-train (5), and an electric vehicle incorporating an electric vehicle transmission of this type.