The shock waves of supernova remnants ( SNRs ) are prominent candidates for the acceleration of the Galactic cosmic rays . SNR RX J1713.7 - 3946 is one well-studied particle accelerator in our Galaxy because of its strong non-thermal X-ray and gamma-ray radiation . We have performed NuSTAR ( 3–79 keV ) observations of the northwest rim of RX J1713.7 - 3946 , where is the brightest part in X-ray and the shock speed is about 4000 km { s } ^ { -1 } . The spatially resolved X-ray emission from RX J1713.7 - 3946 is detected up to 20 keV for the first time . The hard X-ray image in 10–20 keV is broadly similar to the soft-band image in 3–10 keV . The typical spectrum is described by power-law model with exponential cutoff with the photon index \Gamma =2.15 and the cutoff energy \varepsilon _ { c } =18.8 keV . Using a synchrotron radiation model from accelerated electrons in the loss-limited case , the cutoff energy parameter ranges 0.6–1.9 keV , varying from region to region . Combined with the previous measurement of the shock speed , the acceleration of electrons is close to the Bohm-limit regime in the outer edge , while the standard picture of accelerated particles limited by synchrotron radiation in SNR shock is not applicable in the inner edge and the filamentary structure .