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: 52

Answer

$$\frac{d^2y}{dx^2}=6\Big(\cos(3x^2)-6x^2\sin(3x^2)\Big)$$

Work Step by Step

$$\frac{dy}{dx}=(\sin(3x^2))'=\cos(3x^2)(3x^2)'=\cos (3x^2)\cdot 6x=6x\cos(3x^2)$$ $$\frac{dy^2}{dx^2}=\frac{d}{dx}\Big(\frac{dy}{dx}\Big)=(6x\cos(3x^2))'= (6x)'\cos(3x^2)+6x(\cos(3x^2))'= 6\cos(3x^2)+6x(-\sin(3x^2))(3x^2)'= 6(\cos(3x^2)-6x^2\sin(3x^2))$$
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