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: 42



Work Step by Step

Applying the quotient rule, we have $H'(x)=\frac{\frac{d}{dx}(x)\times g(x) f(x)-x\times\frac{d}{dx}(g(x) f(x))}{(g(x) f(x))^{2}}$ $=\frac{g(x) f(x)-x(g'(x)f(x)+g(x)f'(x))}{(g(x)f(x))^{2}}$ (To find the derivative of $g(x)f(x)$, we applied the product rule) $H'(4)=\frac{g(4) f(4)-4(g'(4)f(4)+g(4)f'(4))}{(g(4)f(4))^{2}}$ $=\frac{5\times10-4(-1\times10+5\times-2)}{(5\times10)^{2}}=\frac{13}{250}$
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