In the past I've read that that stuff is more or less just a shorthand for the "formal" definition of a derivative. But I have also seen people solve problems through manipulation of the dx's and the dy's, and treading that as... well as a fraction.
Is there some sort of guide to what you're "allowed" to do with dx and dy in general? Or is the thing basically that people are just "being careful"? This, like discussion of set theory, is always tough because I feel like I'm missing the axioms that could justify certain operations
In the past I've read that that stuff is more or less just a shorthand for the "formal" definition of a derivative. But I have also seen people solve problems through manipulation of the dx's and the dy's, and treading that as... well as a fraction.
Is there some sort of guide to what you're "allowed" to do with dx and dy in general? Or is the thing basically that people are just "being careful"? This, like discussion of set theory, is always tough because I feel like I'm missing the axioms that could justify certain operations