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**MacLaurin Series Integration....**

I have to find the MacLaurin for f(x)=ln(1+x^2)

So i started off by finding the derivative of the function getting

[tex]

\frac{2x}{1+x^2}

[/tex]

My issue lies with the 2x in the numerator. I know how to bring the x into the series, but the two? Do I leave it on the outside or do I bring it in and put it to the nth power? I think my brain is fried, I seem to be getting contradictory information from various sources. So, Im bringing it here and throwing it up on the board.

Should it look like this:

[tex]

\sum_{n=0}^{\infty} (-1)^n x^{2n+1} 2^n

[/tex]

or this:

[tex]

2 \sum_{n=0}^{\infty} (-1)^n x^{2n+1}

[/tex]

Thanks.