SAR ground moving target indicator (GMTI) has long been an important issue for SAR advanced applications. As spatial resolution of space-borne SAR system has been significantly improved recently, the GMTI becomes a very useful tool. Various GMTI techniques have been developed particularly using multi-channel SAR systems. It is, however, still problematic to detect ground moving targets within single channel SAR images while it is not practical to access high resolution multi-channel space-borne SAR systems. Once a ground moving target is detected, it is possible to retrieve twodimensional velocities of the target from single channel space-borne SAR with an accuracy of about 5 % if moving faster than 3 m/s. This paper presents a quick-and-dirty method for detecting ground moving targets from single channel SAR single-look complex (SLC) images by differentiation. Since the signal powers of derivatives present Doppler centroid and rate, it is very efficient and effective for detection of non-stationary targets. The derivatives correlate well with velocities retrieved by a precise method with a correlation coefficient $R^2$ of 0.62, which is well enough to detect the ground moving targets. While the approach is theoretically straightforward, it is necessary to remove the effects of residual Doppler rate before finalizing the ground moving target candidates. The confidence level of results largely depends on the efficiency and effectiveness of the residual Doppler rate removal method. Application results using TerraSAR-X and truck-mounted corner reflectors validated the efficiency of the method. While the derivatives of moving targets remain easily detectable, the signal energy of stationary corner reflectors was suppressed by about 18.5 dB. It results in an easy detection of ground targets moving faster than 8.8 km/h. The proposed method is applicable to any high resolution single channel SAR systems including KOMPSAT-5.