Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises: 1

Answer

$f'(x) = 2x sin (x) + x^{2}cos (x)$

Work Step by Step

$f(x) = x^{2}sin (x)$ Lets use the formula $(fg)' = f'g+ fg'$ $f'(x) = (x^{2}sin (x))' = (x^{2})'sin (x) + x^{2}(sin (x))'$ We know that $(sin (x))' = cos (x)$ So: $f'(x) = (x^{2}sin (x))' = 2x sin (x) + x^{2}cos (x)$
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