In the problem f(x) = -1/x^2+1 finding the derivative using the quotient rule.
the solution would be -x^2+2x-1/(x^2+1)^2?
It seems right but im not sure.
Hold on, you said $\displaystyle f(x) = -\frac{1}{x^2+1}$ in the OP. Which one is correct?
Your differentiating is correct but your simplification on the third line is not - there should be no x term. Plus be more clear with your syntax using brackets
$\displaystyle u = -x \: \rightarrow \: u' = -1$
$\displaystyle v = x^2+1 \: \rightarrow \: v' = 2x$
$\displaystyle f'(x) = \frac{-x^2-1 + 2x^2}{(x^2+1)^2} = \frac{x^2-1}{(x^2+1)^2}$