I think what you suggest is possible, derivation might even be well suited for this application, however I can't tell if it would be better than existing approa

I think what you suggest is possible, derivation might even be well suited for this application, however I can't tell if it would be better than existing approaches. There are some chances that it might be interesting in practice, since it seems that this application of derivatives has not been much studied, but that's highly speculative.