Jade Vanadium

derivatives of inverse trigonometric functions

Hi @Jade Vanadium, and welcome to Wikipedia.

Thanks for your edit to Inverse trigonometric functions § Derivatives of inverse trigonometric functions. I thought the modified version was a bit harder to follow than the original, so I reverted your change, but as a follow-up I rewrote it in yet a third way, as 2 distinct steps. Does that version address your concern about notation? Feel free to make further changes if you think it can still be improved. All the best. –jacobolus (t) 15:50, 18 December 2023 (UTC)

Thanks, I love it! I prefer your update to mine, and it does address my notation concern. My concern was primarily that notation like dx/df(x) is not consistent with the typical definition & notation for differentiation. According to the typical definition, derivative is just an operation applied to a function, and any deviation from that definition is abuse of notation. Even the notation dx/dy (for the derivative of the inverse function) is somewhat abusive, but it's also common enough that students can know what it means, and most teachers will accept it. Notational abuse is not strictly bad, but it is often responsible for confusing students, which is incidentally why I made that edit; a student was confused. Jade Vanadium (talk) 12:01, 22 December 2023 (UTC)

Working with differentials (rather than derivatives) is a fine thing to do, and is not inherently an abuse of notation (indeed, it's the original source of the notation). But it's true that typical introductory calculus courses have some hang-ups about it, due to some unfortunate historical twists and redefinitions. –jacobolus (t) 17:15, 22 December 2023 (UTC)