Find derivative of given function:

\(\displaystyle{f}'{\left({x}\right)}=^{{{1}}}{\frac{{{1}}}{{{x}^{{{2}}}+{1}}}}\dot{{{x}^{{{2}}}+{1}}}'\)

\(\displaystyle={\frac{{{2}{x}}}{{{x}^{{{2}}}+{1}}}}\)

Rules used:

(1) Chain rule

\(\displaystyle{f}'{\left({x}\right)}=^{{{1}}}{\frac{{{1}}}{{{x}^{{{2}}}+{1}}}}\dot{{{x}^{{{2}}}+{1}}}'\)

\(\displaystyle={\frac{{{2}{x}}}{{{x}^{{{2}}}+{1}}}}\)

Rules used:

(1) Chain rule