Independence of Artin L-functions

Let K/Q be a finite Galois extension. Let chi(1),....., chi(r) be r >= 1 distinct characters of the Galois group with the associated Artin L-functions L(s, chi(1)), .....,L(s, chi(r)). Let m >= 0. We prove that the derivatives L-(k) (s, chi(j)), 1 <= j <= r, 0 <= k <= m, are linearly independent over the field of meromorphic functions of order < 1. From this it follows that the L-functions corresponding to the irreducible characters are algebraically independent over the field of meromorphic functions of order < 1.