Es ist

${\displaystyle {}{\begin{aligned}g'(x)&={\frac {n{\left(f(x)\right)}^{n-1}\cdot f'(x)\cdot f(x^{n})-{\left(f(x)\right)}^{n}\cdot f'(x^{n})\cdot nx^{n-1}}{{\left(f(x^{n})\right)}^{2}}}\\&=n{\left(f(x)\right)}^{n-1}\cdot {\frac {f'(x)\cdot f(x^{n})-f(x)f'(x^{n})x^{n-1}}{{\left(f(x^{n})\right)}^{2}}}.\end{aligned}}}$