Total and Partial Differentials as Algebraically Manipulable Entities — mentioned by johnnyb_61820

Sat, 15 Aug 2026 14:15:00 GMT

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

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Total and Partial Differentials as Algebraically Manipulable Entities — mentioned by johnnyb_61820

Wed, 08 Jan 2025 23:05:34 GMT

If you are going to use infinitesimals, though, it requires some additional doing for notation. The standard notation for higher-order derivatives (and partial derivatives) needs to be modified in order for them to work (but they do work great once you do this). Instead of the second derivative being "d^2y/dx^2" it is "(d^2y/dx^2) - (dy/dx)(d^2x/dx^2)" and the differentials can be manipulated just like any other entity. Additionally, you can infer this notation by simply applying the quotient rule to the first derivative (which is a quotient of infinitesimals). See more: "Extending the…

Paper and discussion history. A mention is not an endorsement.

Total and Partial Differentials as Algebraically Manipulable Entities · HackerPapers discussions

Total and Partial Differentials as Algebraically Manipulable Entities — mentioned by johnnyb_61820

Total and Partial Differentials as Algebraically Manipulable Entities — mentioned by johnnyb_61820