  Let $\A$ be a unital complex (Banach) algebra and $\M$ be a unital (Banach)
$\A$-bimodule. The main results describe (continuous) derivations or Jordan
derivations $D:\A\rightarrow \M$ through the action on zero products, under
certain conditions on $\A$ and $\M$. The proof is based on the consideration of
a (continuous) bilinear map satisfying a related condition.
