Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 13 - Section 13.2 - Derivatives and Integrals of Vector Functions - 13.2 Exercise - Page 902: 16

Answer

r'(t)= a x (b + 2tc)

Work Step by Step

r(t)= ta x (b + tc) Using the product rule: r'(t) = (ta)' x (b + tc) + ta x (b + tc)' product rule again and further simplification: r'(t) = (a + a't) x (b + tc) + ta x (b' + (c + tc')) because a, b and c are constant vectors, their derivatives are 0, and the derivative becomes: r'(t) = a x (b + tc) + ta x c Which can be rewritten as: r'(t) = a x (b + tc) + a x tc r'(t)= a x (b + 2tc)
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