  We consider the N=4 supersymmetric Yang-Mills theory in four dimensions. We
compute the one-loop contributions to the effective action with five external
vector fields and compare them with corresponding results in open superstring
theory. Our calculation determines the structure of the F^5 terms that appear
in the nonabelian generalization of the Born Infeld action. The trace operation
on the gauge group indices receives contributions from the symmetric as well as
the antisymmetric part. We find that in order to study corrections to the
symmetrized trace prescription one has to consistently take into account
derivative contributions not only with antisymmetrized products
\nabla_{[\mu}\nabla_{\nu]} but also with symmetrized ones
\nabla_{(\mu}\nabla_{\nu)}.
