Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 147: 85


$5\sqrt {3}$

Work Step by Step

$\frac{d}{dx}(h(\sin x))|_{x=\frac{\pi}{6}}=h'(\sin\frac{\pi}{6})\times \cos \frac{\pi}{6}$ (That is, the derivative of the main function$\times$ the derivative of the inner function) $=h'(0.5)\times\frac{\sqrt 3}{2}=\frac{10}{2}\sqrt 3=5\sqrt 3$
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