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by johnnyb_61820 525 days ago
What I did in my book to keep everything algebraic but not introduce weird notation is just set the derivative equal to a variable. So, say m = dy/dx. Then, the second derivative is just dm/dx.

The advantage to the revised notation is that you can describe things that are difficult or impossible to describe in the other notation. For example, you can legitimately look at d^2y/d^2x (note the placement of the 2 on the denominator to see how this is different). This is a valid ratio under my system but invalid under the standard system (though I actually consider my system to be the standard system just with prior mistakes corrected).