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: 27

Answer

$\frac{dy}{dx}=3x^{2}\sin^2(5x)+10x^3\sin(5x)\cos(5x)$

Work Step by Step

$y=x^3sin^2(5x)$ $\frac{dy}{dx}=3x^{3-1}\times{sin^2(5x)}+(x^3\times2sin(5x)\times{cos(5x)}\times5)$ $\frac{dy}{dx}=3x^{2}sin^2(5x)+10x^3sin(5x)cos(5x)$
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