WolframAlpha blows simple substitution? I am to find a formula for the n-th derivative of $$\frac{1+x}{1-x}$$ I came up with $$\frac{(-1)^{n+1} \times 2 \times n!}{(1-x)^{n+1}}$$
This seems right, but I noticed that WolframAlpha somehow manages to eat the sign for any n.
For example, for $n=2$ I have: $\frac{-4}{(1-x)^{3}}$, but WolframAlpha gives $\frac{4}{(1-x)^3}$. I am not particularly good at calculating, but I would like to think that I have mastered the numbers below $10$ so I'm pretty sure I'm right here and WolframAlpha did something very weird.
EDIT: Yep, my derivative is wrong. BUT this still doesn't answer the question why WolframAlpha responds with a positive fraction all the time - I didn't ask it to calculate a derivate, I just entered my formula.
PS: Who removed my WolframAlpha input? That was sort of essential to the question, I was never that interested in the derivative itself, I just wanted to know why WA responded that way.
(Exact input: (-1)^(n+1)*2*n!/((1-x)^(n+1)), n=2 )

Hint 
$$\frac{1+x}{1-x}= \frac{2-(1-x)}{1-x}=\frac{2}{1-x} -1$$
This makes the problem easier to derivate. I think WA is right, you probably forgot to multiply by the derivative of $(1-x)$ at some point....
