A portable, automated chemical analyzer having a polarographic oxygen electrode submerged in a batch of stirred solution. The signal from the electrode is directly differentiated and amplified to produce a signal proportional to the time rate of change of oxygen concentration. The membrane of the polarographic sensor is stretched very tightly over the cathode surface to provide a high signal-to-noise ratio. Methods for analyzing cholesterol-cholesterol oxidase and various other enzyme systems by the polarographic electrode oxygen sensing apparatus include the steps of converting the sensed signal into time rate of change of oxygen concentration and recording the maximum rate of change of oxygen concentration.