Re:Learning algebra in my 60s
by thaumasiotes on Monday August 08, 2022 @04:53PM
(#32390878)
> I took my AP Calculus class in my senior year of high school and my teacher (fantastic man) showed us how the formula for a derivative is derived.
This is pretty easy to do for a polynomial term, but much harder for x raised to a non-integer power[1], or sin(x). There is no one way to "derive the formula for a derivative"; different functions have to be analyzed differently.
[1] Wikipedia suggests that the simplest way to derive this formula is to begin by establishing that exp(x) is its own derivative. But that's not an approach I'd be likely to take with students new to calculus.
Re:Learning algebra in my 60s
by jjice on Tuesday August 09, 2022 @12:30AM
(#32394162)
I'm no math pro, so my terminology is probably way off. I just remember a lot of h(x) in there and showing why that makes sense in the context of what a derivative is.
This is pretty easy to do for a polynomial term, but much harder for x raised to a non-integer power[1], or sin(x). There is no one way to "derive the formula for a derivative"; different functions have to be analyzed differently.
[1] Wikipedia suggests that the simplest way to derive this formula is to begin by establishing that exp(x) is its own derivative. But that's not an approach I'd be likely to take with students new to calculus.