Myers and Lahoda (1975) gave special emphasis to the problem of estimation of the lower order partial derivatives of a higher order response function. This article addresses the same problem. We obtain a class of estimators of the lower order partial derivatives of a higher order response function using Bock's (1975) approach. For a wide class of conditions our estimators have a smaller integrated mean squared errors than the minimum bias estimator developed by Karson, Manson and Hader (1969).