Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 19

Answer

$f'(x)=\frac{-3sin(3\sqrt x)cos(3\sqrt x)}{\sqrt x}$

Work Step by Step

$f(x)=cos^2(3\sqrt x)$ $f(x)=cos^2(3x^{\frac{1}{2}})$ $f'(x)=2cos^{2-1}(3\sqrt x)\times(\frac{d}{dx})(cos(3\sqrt x)))$ $f'(x)=2cos^{2-1}(3\sqrt x)\times(-sin(3\sqrt x))\times(\frac{d}{dx})(3x^{\frac{1}{2}})$ $f'(x)=2cos^1(3\sqrt x)\times(-sin(3\sqrt x))\times(\frac{3}{2}x^{\frac{1}{2}-1})$ $f'(x)=-sin(3\sqrt x)2cos(3\sqrt x)\times(\frac{3}{2}x^{\frac{-1}{2}})$ $f'(x)=\frac{-6sin(3\sqrt x)cos(3\sqrt x)}{2\sqrt x}$ $f'(x)=\frac{-3sin(3\sqrt x)cos(3\sqrt x)}{\sqrt x}$
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