Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - Chapter 2 Review Exercises - Page 184: 15

Answer

$f''(x) = 4xcos(x)-(x^2-2)sin(x)$

Work Step by Step

a) Using WolframAlpha and inputting "limit ((x+h)^2 * sin(x+h)-(x^2+sin(x)))/h as h approaches 0", we get $f'(x) = x(2sin(x)+xcos(x))$. b) $f'(x) = 2x(sin(x)) + cos(x)*x^2 = x(2sin(x)+xcos(x))$ c) Using WolframAlpha and inputting "derivative of x(2sin(x)+xcos(x))", we get $f''(x) = 4xcos(x)-(x^2-2)sin(x)$
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