Nonparametric estimators are frequently criticized for their poor performance in small samples. In this paper, the author considers using kernel methods for the estimation of the expected derivatives of a regression function. The proposed estimators are shown to be asymptotically normal and n-consistent. As a consequence, their standard errors are comparable to parametric estimates. An empirical example demonstrates the facility of the approach. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.