Answer
$y'=-\dfrac{x^{4}+3x^{2}+2x}{(x^{3}-1)^{2}}$
Work Step by Step
$y=\dfrac{x^{2}+1}{x^{3}-1}$
Differentiate using the quotient rule:
$y'=\dfrac{(x^{3}-1)(x^{2}+1)'-(x^{2}+1)(x^{3}-1)'}{(x^{3}-1)^{2}}=...$
$...=\dfrac{(x^{3}-1)(2x)-(x^{2}+1)(3x^{2})}{(x^{3}-1)^{2}}=...$
Evaluate the products and simplify
$...=\dfrac{2x^{4}-2x-3x^{4}-3x^{2}}{(x^{3}-1)^{2}}=\dfrac{-x^{4}-3x^{2}-2x}{(x^{3}-1)^{2}}=-\dfrac{x^{4}+3x^{2}+2x}{(x^{3}-1)^{2}}$
