The ratio estimation problem of probability density function partial derivatives under the assumption of asymptotic decay of the dependence between observations is solved. The convergence rate for estimators of probability density function partial derivatives and its ratios are established. The main part of asymptotic mean square error of the piecewise smooth approximation of the ratio substitution estimator is found. These results are applied to the ratio estimation of derivatives of the probability density of errors in stochastic regression processes. Copyright 2002 IFAC