  We study Whitehead products in the rational homotopy groups of a general
component of a function space. For the component of any based map f: X \to Y,
in either the based or free function space, our main results express the
Whitehead product directly in terms of the Quillen minimal model of f. These
results follow from a purely algebraic development in the setting of chain
complexes of derivations of differential graded Lie algebras, which is of
interest in its own right. We apply the results to study the Whitehead length
of function space components.
