I'm trying to calculate the Taylor series of $arcsin(1-x)$ about $x=0$. I'm having trouble because I can't compute the derivative there.
I can see the correct solution on WolframAlpha (http://www.wolframalpha.com/input/?i=taylor+series+arcsin(1-x)), but I'd like to know how to derive it. I found a similar question regarding the Taylor series for arccos(1-x) (Taylor expansion of $\arccos(1-x)$ around $x=0$ to two terms), but the derivation takes advantage of the fact that $arccos(1-x) << 1$, which is not the case for arcsin.
Any help would be greatly appreciated.