  Let $G$ be a finite solvable group and $\chi, \psi \in \Irr(G)$ be complex
characters of $G$. Let $\alpha$ be an irreducible constituent of the product
$\chi \psi$. We show that the derived length of $\Ker(\alpha)/\Ker(\chi\psi)$
is bounded by a linear function on the number of distinct irreducible
constituents of $\chi\psi$
