Answer
$\frac{4w}{(w^2+1)^2}$
Work Step by Step
$\left(\frac{f}{g}\right)'$ = $\frac{f'g-fg'}{g^2}$
$\frac{w^2-1}{w^2+1}$ = $\frac{(2w)(w^2+1)-(w^2-1)(2w)}{(w^2+1)^2}$ = $\frac{4w}{(w^2+1)^2}$
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