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: 36

Answer

$$\frac{dy}{dx}=(x^2+x)^4\sin^7x(5(2x+1)\sin x+8(x^2+x)\cos x)$$

Work Step by Step

$$\frac{dy}{dx}=((x^2+x)^5\sin^8x)'=((x^2+x)^5)'\sin^8x+(x^2+x)^5(\sin^8x)'= 5(x^2+x)^4(x^2+x)'\sin^8x+(x^2+x)^5\cdot8\sin^7x(\sin x)'= 5(x^2+x)^4(2x+1)\sin^8x+8(x^2+x)^5\sin^7x\cos x= (x^2+x)^4\sin^7x(5(2x+1)\sin x+8(x^2+x)\cos x)$$
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