I will describethe derived Hecke algebrain the case of weight one forms and how, in this setting, it is conjecturally related to Stark units. I will then describe some joint work with Henri Darmon, Michael Harris,and Victor Rotgerwhere we establish this relationship for dihedral forms. The proof involves recent ideas of E. Lecouturier about the Eisenstein ideal, and the derivative of the Riemann zeta function at -1 (in the sense of Mazur-Tate) plays an important role.