Science:Math Exam Resources/Courses/MATH100/December 2011/Question 01 (f)/Solution 1

Using the quotient rule we compute

${\begin{aligned}\left({\frac {x}{x^{2}-1}}\right)'&={\frac {(1)(x^{2}-1)-(2x)(x)}{(x^{2}-1)^{2}}}\\&={\frac {x^{2}-1-2x^{2}}{(x^{2}-1)^{2}}}\\&=-{\frac {x^{2}+1}{(x^{2}-1)^{2}}}\end{aligned}}$