Calculus 8th Edition

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

Chapter 13 - Vector Functions - 13.2 Derivatives and Integrals of Vector Functions - 13.2 Exercises - Page 900: 11

Answer

$2t$ i $-2t sin (t^2)$ j +$2 sin(t) cos(t)$

Work Step by Step

Take derivatives component-by-component. Derivative of $t^2$ is $2t$ by power rule, derivative of $cos (t^2)$ is $-2t sin(t^2)$ by trig derivatives and chain rule, derivative of $(sin(t))^2$ is $2 sin(t) cos(t)$ by trig derivatives and chain rule.
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