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In this paper, a robust nonparametric derivative estimator is proposed to estimate the derivative function of nonparametric regression when the data contain noise and have curves. A robust estimation of the derivative function is important for understanding trend analysis and conducting statistical inferences. The methods for simultaneously assessing the functional relationship between response and covariates as well as estimating its derivative function without trimming noisy data are quite limited. Our robust nonparametric derivative functions were developed by constructing three weights and then incorporating them into kernel-smoothing. Various simulation studies were conducted to evaluate the performance of our approach and to compare our proposed approach with other existing approaches. The advantage of our robust nonparametric approach is demonstrated using epidemiology data on mortality and temperature in Seoul, South Korea. [ABSTRACT FROM AUTHOR]