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

question 84

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) \(\frac{7 x^{8}-8 x^{7}-1}{3\left(x^{8}+1\right)(x-1)}\)

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