Answer
The derivative is $3x^2cos(x)-x^3sin(x)$.
Work Step by Step
Product Rule $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=x^3 ;u’(x)= 3x^2$
$v(x)= cos(x);v’(x)= -sin(x)$
$f'(x)=(3x^2)(cos(x))+(x^3)(-sin(x))=3x^2cos(x)-x^3sin(x)$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 2 - Differentiation - 2.3 Exercises - Page 125: 5
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