Electron energy distribution function (EEDF) is a key parameter of plasmas, which is directly proportional to the second derivative of the probe I-V characteristics. Because of an amplifying effect of unavoidable noises in the experimental prolbe I-V curves during the derivation process, the experimental I-V curves should be smoothed before performing the numerical derivation. This paper investigates the effect of adjustable factors used in the smoothing process on the deduced second derivative of the I-V curves, and an optimum group of the adjustable factors is selected to make the rms deviation of the smoothed I-V curves from the measured curves less than 1%. A simple differentiation circuit is designed and used to measure the EEDF parameter straightforwardly. It is the first time, so far as we know,to measure the EEDF parameters simultaneously by means of both numerical and circuit derivative methods under the same discharge conditions and on the same discharge equipment. The deviation between two groups of mean electron energy E and electron density ne obtained by the above different methods is within about 7%. This apparently improves the reliability of the measurements of the EEDF parameters.