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: 8

Answer

$ f’(x) =-\frac{x^{2}+8x+3}{(x^{2}+x+1)^{2}} $

Work Step by Step

$Quotient$ $Rule:$ $ (\frac{f}{g})’ = \frac{gf’-fg’}{g^{2}} $ $ f(x) = \frac{x+4}{x^{2}+x+1} $ $ f’(x) = \frac{(x^{2} +x+1)(1)-(x+4)(2x+1)}{(x^{2}+x+1)^{2}} $ $ f’(x) =\frac{-x^{2}-8x-3}{(x^{2}+x+1)^{2}} $
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