#### Answer

$f’(-2) = -\frac{11}{169} $

#### Work Step by Step

$f(x) = \frac {x}{3x^2 +1} $
Quotient Rule:
$f’(x) = \frac{(3x^2 +1)(1) - (x)(6x)}{(3x^2+1)^2} $
$f’(x) = \frac{-3x^2 +1}{(3x^2+1)^2 }$
Evaluate f’(x) at x=-2:
$f’(-2) = \frac{-3(-2)^2 +1}{(3(-2)^2+1)^2} $
$f’(-2) = \frac{-11}{169} $