  Certain two and three point functions of gauge invariant primary operators of
${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the
$\th$-components. This allows one to read off many component descendent
correlators. Our results show the only possible $g^2_{YM}$ corrections to the
free field correlators are contact terms. Therefore they vanish for operators
at separate points, verifying the known non-renormalization theorems. This also
implies the results are consistent with ${\cal N}=4$ supersymmetry even though
the Lagrangian we use has only ${\cal N}=1$ manifest supersymmetry. We repeat
some of the calculations using supersymmetric Landau gauge and obtain, as
expected, the same results as those of supersymmetric Feynman gauge.
