Derivative

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I need to find the derivative of (x) / (x^2 +1)
I got x^2 + 1(1) - x(2x) all divided by (x^2 +1)^2. Now I just need to simplify it and I think I'm complicating things for myself. The final function I ended up with the first time around was (-2x^2) / (x^2+ 1). Then I tried doing something different and ended up with another completely different function. Sorry for the petty problem, but I can't get out of my own head and really don't want to get this wrong. Any help's appreciated!

  • Derivative -

    (x^2+1)(1)-x (2x) /(x^2+1)^2
    =

    -(x^2 -1) /(x^2+1)^2

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