The derivative-like line shape is a result of the use of field modulation. In order to get sufficient signal to noise, the B_0 field (large, static field) is modulated (usually at 100kHz) and a lock-in amplifier (or equivalent) is used to reject any frequencies beside 100kHz. The result of this field modulation is that the signal that is obtained is not the value of the absorbance, rather the difference in the absorbances between the ends of the modulation amplitude (more or less) i.e. ~d(absorption)/dB. A slightly more detailed explanation (with a picture, figure 2.7) is here.
There are lots of caveats and such due to the fact that it's not a true derivative, and there is, therefore, some signal distortion.
There is currently (again) development of detection techniques which are not dependent on the modulation of the field for S/N.