Use logarithmic differentiation to find the derivative of the function.

$y=\sqrt[4]{\frac{x^{5}1}{x-1}}$

$\frac{8x^9-9x^{8}1}{4(x^{9}1{)}^{\frac{3}{4}}(x-1{)}^{\frac{8}{4}}}$

$\frac{8x^2-9x^8-1}{4(x^{9}1)(x-1)}$

$\frac{8x^9-9x^{8}1}{4(x^{9}1)(x-1)}$

$\frac{8x^2-9x^8-1}{4(x^{9}1{)}^{\frac{3}{4}}(x-1{)}^{\frac{8}{4}}}$