Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises: 20

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} $
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