With the increase interest in nuclear data sensitivity and uncertainty analysis, Many researches have developed new methods that can be used to perform sensitivity analysis for different response functions. In previous researches, several methods have been developed in the continuous-energy Reactor Monte Carlo code (RMC) to perform sensitivity analysis of the effective multiplication factor (keff), reaction rate ratios and bilinear response functions. Due to the fact that the reaction rates are also common and important generalized response functions, some methods suitable for its sensitivity and uncertainty analysis need to be developed. In this work, the differential operator method was investigated and implemented in RMC to perform sensitivity analysis of reaction rate. The new capability in RMC are tested on Godiva and Flattop benchmark problems. For the Godiva benchmark, the sensitivity coefficients of fission rate and absorption rate calculated by the newly developed differential operator method in RMC are compared with the reference results from McCARD. For the Flattop benchmark, the sensitivity coefficients of fission rate and absorption rate produced by differential operator method are compared with reference results produced by the direct perturbation method. In general, results produced by the differential operator method agree well with reference results, which verifies the correctness of newly developed differential operator method in performing sensitivity analysis of reaction rates. Moreover, based on sensitivity coefficients calculated by the differential operator method (DOM), the first-order uncertainty quantification method are also developed in RMC to perform uncertainty analysis of reaction rates. The uncertainties of fission rate and absorption rate calculated by first-order uncertainty quantification method and stochastic sampling method are compared. Fairly good agreement can be observed from these uncertainty results.