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: 22

Answer

$f'(x)=-\frac{3\sin\left(\frac{x}{x+1}\right)\cos^2\left(\frac{x}{x+1}\right)}{{(x+1)^2}}$

Work Step by Step

$f(x)=cos^3(\frac{x}{x+1})$ $f'(x)=3cos^2(\frac{x}{x+1})\times\frac{dy}{dx}cos(\frac{x}{x+1})$ $f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{1\times{x+1}-(x\times1)}{(x+1)^2}$ $f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{{x+1}-x}{(x+1)^2}$ $f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{1}{(x+1)^2}$ $f'(x)=-\frac{3\sin\left(\frac{x}{x+1}\right)\cos^2\left(\frac{x}{x+1}\right)}{{(x+1)^2}}$
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