We know that the derivative of $\ln(u)$ is $\frac{1}{u} \cdot u'$, where $u'$ is the derivative of $u$ with respect to $x$. Here, $u = 1 + x^{2}$, so $u' = 2x$. Therefore, the first derivative of $f(x)$ is:
$$f'(x) = \frac{1}{1+x^{2}} \cdot 2x =
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