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 - Page 136: 60


$y'=3+10\pi^2 x\sin{(\pi x)}^2.$

Work Step by Step

$y=f(x)+g(x)\rightarrow f(x)=3x$; $g(x)=-5\cos{(\pi x)}^2$ Using Power Rule: $f'(x)=3$ Using Chain Rule: $u=(\pi x)^2$; $\dfrac{du}{dx}=2\pi^2x$ $g(u)=-5\cos{u};\dfrac{d}{du}g(u)=5\sin{u}$ $\dfrac{d}{dx}g(x)=\dfrac{d}{du}g(u)\times\dfrac{du}{dx}=10\pi^2 x\sin{(\pi x)}^2.$ $y'=f'(x)+g'(x)=3+10\pi^2 x\sin{(\pi x)}^2.$
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