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 - Page 158: 35


$$\frac{dy}{dx}=(5x+8)^6(1-\sqrt x)^5(35(1-\sqrt x)-\frac{3}{\sqrt x}(5x+8))$$

Work Step by Step

$$\frac{dy}{dx}=((5x+8)^7(1-\sqrt x)^6)'=((5x+8)^7)'(1-\sqrt x)^6+(5x+8)(1-\sqrt x)^6)'=7(5x+8)^6\cdot(5x+8)'(1-\sqrt x)^6+(5x+8)^7\cdot6(1-\sqrt x)^5\cdot(1-\sqrt x)'= 35(5x+8)^6(1-\sqrt x)^6-\frac{3}{\sqrt x}(5x+8)^7(1-\sqrt x)^5= (5x+8)^6(1-\sqrt x)^5(35(1-\sqrt x)-\frac{3}{\sqrt x}(5x+8))$$
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