Use Logarithmic Differentiation to Find the Derivative of the Function $y=\sqrt[3]{\frac{x^{8}+1}{x-1}}$

Multiple Choice

Use logarithmic differentiation to find the derivative of the function. $y=\sqrt[3]{\frac{x^{8}+1}{x-1}}$

A) $\frac{7 x^{8}-8 x^{7}+1}{3\left(x^{8}+1\right) ^{2 / 3}(x-1) ^{4 / 3}}$
B) $\frac{7 x^{8}-8 x^{7}-1}{3\left(x^{8}+1\right) ^{2 / 3}(x-1) ^{4 / 3}}$
C) $\frac{7 x^{8}-8 x^{7}+1}{3\left(x^{8}+1\right) (x-1) }$
D) $\frac{7 x^{8}-8 x^{7}-1}{3\left(x^{8}+1\right) (x-1) }$