  The computation of higher derivative corrections to the low energy effective
actions of ${\cal N}=2$ gauge theories is considered. In particular, higher
derivative corrections are computed for four dimensional ${\cal N}=2$ super
Yang-Mills theory with gauge group SU(2) and $N_f=4$ hypermultiplets in the
fundamental representation. The four derivative terms computed in an approach
which realizes the gauge theory as the world volume theory of three branes in F
theory are in agreement with the field theory result.
