  For transcendental values of $q$ all bicovariant first order differential
calculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and
$Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first
order calculi are determined by an irreducible corepresentation of the quantum
group and a complex number $\zeta$ such that $\zeta^{n+1}=1$ for $SL_q(n+1)$
and $\zeta^2=1$ for $Sp_q(2n)$. Any bicovariant calculus is inner and its
quantum Lie algebra is generated by a central element. The main technical
ingredient is a result of the Hopf algebra $R(G_q)^0$ for arbitrary simple Lie
algebras.
