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We present a time-dependent spot modeling analysis of 15 consecutive years of V-band photometry of the long-period (Porb = 28.6 days) RS CVn binary HR 7275. This baseline in time is one of the longest, uninterrupted intervals a spotted star has been observed. The spot modeling analysis yields a total of 20 different spots throughout the time span of our observations. The distribution of the observed spot migration rates is consistent with solar-type differential rotation and suggests a lower limit of the differential-rotation coefficient of 0.022 +/-0.004. The observed, maximum lifetime of a single spot (or spot group) is 4.5 years, the minimum lifetime is approximately one year, but an average spot lives for 2.2 years. If we assume that the mechanical shear by differential rotation sets the upper limit to the spot lifetime, the observed maximum lifetime in turn sets an upper limit to the differential-rotation coefficient, namely 0.04 +/- 0.01. This would be differential rotation just 5 to 8 times less than the solar value and one of the strongest among active binaries. We found no conclusive evidence for the existence of a periodic phenomenon that could be attributed to a stellar magnetic cycle.