Chapter 11 - Section 11.3 - The Product and Quotient Rules - Exercises - Page 818: 52

$\displaystyle \frac{-2}{x^{3}}$

Simplify the function... $y=\displaystyle \frac{1-\frac{1}{x^{2}}}{x^{2}-1}=\frac{\frac{x^{2}-1}{x^{2}}}{x^{2}-1}=\frac{(x^{2}-1)}{x^{2}(x^{2}-1)}=x^{-2}$ $\displaystyle \frac{dy}{dx}=-2x^{-3}=\frac{-2}{x^{3}}$