Conformal Dimensions of Two-Derivative BMN Operators

We compute the anomalous dimensions of BMN operators with two covariant derivative impurities at the planar level up to first order in the effective coupling lambda'. The result equals those for two scalar impurities as well as for mixed scalar and vector impurities given in the literature. Though the results are the same, the computation is very different from the scalar case. This is basically due to the existence of a non-vanishing overlap between the derivative impurity and the ``background'' field Z. We present details of these differences and their consequences.