Hey guys so I'm really confused as I wasn't shown any examples other than what it means to be self-adjoint and what L2 means so I have no idea how to get this problem started. Any step by step approach would be reeeeally helpful and very much appreciated.

Consider the linear operatior A= d/dx acting on smooth functions u(x) L^2[0,1] satisfying the boundary conditions u(0) = 2u(1) on 0,1]. Use the usual inner product on L^2[0,1] to find the adjoint of A and its domain.