Kähler covariant derivative of a superpotential ($D_{i}W={\partial }_{i}W+K_{i}W$)

The Kähler covariant derivative of a superpotential transforms by the same holomorphic factor as the superpotential under a Kähler transformation. This follows by differentiating $e^{-f}W$ and cancelling the extra derivative of $f$ against the shift of $K_i$.