  Let A be a coquasitriangular Hopf algebra and X the subalgebra of A generated
by a row of a matrix corepresentation u or by a row of u and a row of the
contragredient representation u^c. In the paper left-covariant first order
differential calculi on the quantum group A are constructed and the
corresponding induced calculi on the left quantum space X are described. The
main tool for these constructions are the L-functionals associated with u. The
results are applied to the quantum homogeneous space GL_q(N)/GL_q(N-1).
