On the second derivative side, a fuller treatment (including applying the approach to partial differentials) is given in the paper "Total and Partial Differenti

On the second derivative side, a fuller treatment (including applying the approach to partial differentials) is given in the paper "Total and Partial Differentials as Algebraically Manipulable Entities". https://arxiv.org/abs/2210.07958 https://arxiv.org/abs/2210.07958