Talk:Power Rule for Derivatives

Question: "Shouldn't this be a mapping from $\R \to X$, $X \subset \R$, or something like that?"

Not the way I see it. The mapping is from the whole of $\R$ (which is the domain) to the whole of $\R$ (which is the codomain) and $f$ may or may not be a surjection in which case the image of $f$ will be a subset of $\R$. --prime mover 16:39, 9 November 2011 (CST)

Err I typed it wrong, I meant the domain. But I'm thinking of functions like $f(x) = x^{1/2}$ --GFauxPas 16:41, 9 November 2011 (CST)

Bah, you have got to strive for accuracy!

Okay, the domain is not technically the "whole" of $\R$ - for certain values of $n$ there are points where it's not defined, particuarly where $x$ is negative, but at this stage of approximation the terminology is adequate.

If you like you can write a thesis on exactly what values of $x$ and $n$ the function is valid for. If you can sort that out rigorously, then you can add a link to it from a note about the validity of the domain. --prime mover 16:44, 9 November 2011 (CST)