Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises: 48

Answer

$y'=4(1-2x)\sin{(1-2x)}^2$.

Work Step by Step

$u=(1-2x)^2$; $\dfrac{du}{dx}=-4(1-2x)$. $\dfrac{dy}{du}=-\sin{u}$. $\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=4(1-2x)\sin{(1-2x)}^2$ . Note: $\dfrac{du}{dx}$ is found using the Chain Rule as follows: $\dfrac{du}{dx}=(-2)(2)(1-2x)^{2-1}=-4(1-2x).$
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