Use Logarithmic Differentiation to Find the Derivative of the Function $y=\sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$

Multiple Choice

Use logarithmic differentiation to find the derivative of the function. $y=\sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$

A) $y^{\prime}=-\frac{9 x}{\left(x^{4}-1\right) } \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$
B) $y^{\prime}=\frac{9 x}{4 x^{4}-1} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$
C) $y^{\prime}=-\frac{36 x}{x^{4}-1} \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$
D) $y^{\prime}=-\frac{36 x}{x^{4}-1}$
E) $y^{\prime}=-\frac{4 x}{9\left(x^{4}-1\right) } \sqrt[9]{\frac{x^{2}+1}{x^{2}-1}}$