By plotting the derivative you can find out the value of electrical and magnetic susceptibility which can further help you to analyze the spin glass transitions at different temperature ...............
The physical elements of the M(H) derivative are the reversible susceptibility near saturation or reversals, and the irreversible susceptibility due to domain cooperation. If you plot the normal susceptibility, delta M/ delta H you may find XN(M) to be linear as in our cooperative model. This seems to describe both magnetic and electric hysteresis. Nonlinearity is due to nucleation and denucleation of domain walls beyond the coercive field Hc. I assume negligible demagnetizing field, stress, viscosity and eddy current effects.