1. Deriving Taylors for 1/(1-X)

I am currently deriving Taylors for all n. I had to do one for 1/(1-x) and I came up with 1-x+x^2-x^3+x^4 instead of 1+x^2+x^3+x^4+...+x^n. When I take the derivatives of (1-x)^-1 I get F'= -(1-x)^-2 F''= 2(1-x)^3 F'''=-6(1-x)^4. Where am I going wrong?

2. Originally Posted by manyarrows
I am currently deriving Taylors for all n. I had to do one for 1/(1-x) and I came up with 1-x+x^2-x^3+x^4 instead of 1+x^2+x^3+x^4+...+x^n. When I take the derivatives of (1-x)^-1 I get F'= -(1-x)^-2 F''= 2(1-x)^3 F'''=-6(1-x)^4. Where am I going wrong?
$\frac{d}{dx}\frac{1}{1-x}= \left(\frac{d}{dx}(1-x)\right) \frac{-1}{(1-x)^2}=\frac{1}{(1-x)^2}$

CB

3. Duh

Im so used to seeing the (x-1) in the denominator I just take it for granted the derivative is 1. I definitly need to pay more attention to detail. Thanks.