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 - Page 122: 39


$(fg)'(4)=-20$ $(f/g)'(4)=0$

Work Step by Step

Using the product rule, we have $(fg)'(4)=g(4)\cdot f'(4)+f(4)\cdot g'(4)=(5\times-2)+(10\times-1)=-20$ Using the quotient rule, we obtain $(\frac{f}{g})'(4)=\frac{g(4)\cdot f'(4)-f(4)g'(4)}{(g(4))^{2}}=\frac{(5\times-2)-(10\times-1)}{5^{2}}=0$
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