Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 142: 71

Answer

$f'(4)=16$

Work Step by Step

Given, $f(x)=\sqrt x g(x), g(4)=8, \&g'(4)=7.$ Differentiating $f$ with respect to $x$, keeping chain rule as well as product rule in mind, $$f'(x)=\frac{1}{2\sqrt x}g(x)+\sqrt x g'(x)$$At $x=4$, $$f'(4)=\frac{1}{2\sqrt4}g(4)+\sqrt 4 g'(4)=\frac{8}{4}+2\times7$$ $$f'(4)=2+14=16.$$
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