  We generalize the proof of the non-renormalization of the four derivative
operators in ${\cal N}=4$ Yang Mills theory with gauge group SU(2) to show that
certain terms with 2N derivatives are not renormalized in the theory with gauge
group SU(N). These terms may be determined exactly by a simple perturbative
computation. Similar results hold for finite ${\cal N}=2$ theories. We comment
on the implications of these results.
