Answer
$f'(t)=2t^4(5\cos{t}-t\sin{t}).$
Work Step by Step
Product Rule $f'(t)=((u(t)(v(t))’=u’(t)v(t)+u(t)v’(t))$
$u(t)=2t^5 ;u’(t)=10t^4 $
$v(t)=\cos{t} ;v’(t)=-\sin{t} $
$f'(t)=(10t^4)(\cos{t})+(-\sin{t})(2t^5)$
$2t^4(5\cos{t}-t\sin{t}).$
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 - Review Exercises - Page 157: 32
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