`y = ln root(3)((x - 1)/(x + 1))` Find the derivative of the function.

$\displaystyle{y}={\ln{{\sqrt[{\frac{{1}}{{3}}}]{{\frac{{{x}-{1}}}{{{x}+{1}}}}}}}}$

$\displaystyle{y}={{\ln{{\left({x}-{1}\right)}}}}^{{\frac{{1}}{{3}}}}-{{\ln{{\left({x}+{1}\right)}}}}^{{\frac{{1}}{{3}}}}$

$\displaystyle{y}=\frac{{1}}{{3}}{\ln{{\left({x}-{1}\right)}}}-\frac{{1}}{{3}}{\ln{{\left({x}+{1}\right)}}}$

$\displaystyle{y}'=\frac{{1}}{{{3}{\left({x}-{1}\right)}}}-\frac{{1}}{{{3}{\left({x}+{1}\right)}}}$

$\displaystyle{y}'=\frac{{{\left({x}+{1}\right)}-{\left({x}-{1}\right)}}}{{{3}{\left({x}-{1}\right)}{\left({x}+{1}\right)}}}$

$\displaystyle{y}'=\frac{{{x}+{1}-{x}+{1}}}{{{3}{\left({x}-{1}\right)}{\left({x}+{1}\right)}}}$

$\displaystyle{y}'=\frac{{2}}{{{3}{\left({x}-{1}\right)}{\left({x}+{1}\right)}}}$

The derivative of function y is $\displaystyle\frac{{2}}{{{3}{\left({x}-{1}\right)}{\left({x}+{1}\right)}}}$ .

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