You can analize these curves as any other derivative: it could help to evaluate the rate of approach to saturation, the coercive field vs. maximum B change; and so on. It will depend on what you are looking for.

Hope this helps.

In words, you  would call this "differential susceptibility".

What we normally call "susceptibility" is dM/dH at H=0 (zero field susceptibility).

A simple example: as long as dM/dH = M(H)/H, you have a linear M(H) relationship. Other than that, G.F. Goya's comment is just right. One way to make use of that is the following: If you have a physical model (equation) for M(H), then you can calculate the derivative and compare this to you expectation. This can be useful in M(H) measurements, where e.g. the exact subtraction of a diamagnetic "background" contribution is difficult. Since that islinear in H, it contributes only as a constant to dM/dH.

The dM/dH curves reflect the the magnetic susceptibility vs H. You may examine  it primary values at H=0, then it maximum value. This values play a great role for the technical using some magnetic materials. For paramagnetics you may measure the linear relationship between magnetic susceptibility and H/

Your plots suggests that you are using different samples. Which instrument you are using? Is there is default measurements for DM/DH ?

If your sample is ferromagnetic then from the plots you may get squareness ratio of hysterisis loop, you may get information about particle size distribution.

Normally as expressed by other experts , one can get susceptibility.

Previous answers are perfectly correct for samples with unique dependence of M vs. H, i.e. those without hysteresis.  Here, there is no difference between collecting M(H) data first and differentiating them in the second step, or measuring directly dM/dH during field sweep.  Well, different modulation frequencies may (and most often will) produce different results.  When the sample is hysteretic, then it is indeed unclear what is being measured during direct collection of dM/dH data.  This is because the results depend sensitively on previous (magnetic and thermal) history of the sample. Taking major hysteresis loop and differentaiting it (preferably its lower branch) will give you something called switching field distribution (SFD).   This is what do you most likely see in the last row of the figure presented.  Physical interpretation of SFD is not an easy task.  It is usually related to the strength of domain walls' pinning but there are other explanations possible.

In the case of metamagnetic transition, from the dm/dh vs h plot you will get the critical field that is required for metamagnetic transition