  The derivations of a left coideal subalgebra B of a Hopf algebra A which are
compatible with the comultiplication of A (that is, the covariant first order
differential calculi, as defined by Woronowicz, on a quantum homogeneous space)
are related to certain right ideals of B. The correspondence is one-to-one if A
is faithfully flat as a right B-module. This generalizes the result for B=A due
to Woronowicz. A definition for the dimension of a first order differential
calculus at a classical point is given. For the quantum 2-sphere S(q,c) of
Podles under the assumptions "q is not a root of unity" and "c is not equal to
-q^(2n)/(q^(2n)+1)^2" for all n=0,1,..., three 2-dimensional covariant first
order differential calculi exist if c=0, one exists if c=-q/(q+1)^2 or
c=q/(-q+1)^2 and none else. This extends a result of Podles.
