Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Section 13.2 - Derivatives and Integrals of Vector Functions - 13.2 Exercise - Page 860: 15

Answer

As a result $\boldsymbol{r'}(t)=\boldsymbol{b}+2t\boldsymbol{c}$.

Work Step by Step

$\boldsymbol{r}(t)=\boldsymbol{a}+t\boldsymbol{b}+t^2\boldsymbol{c}$ In order to compute $\boldsymbol{r'}(t)$ we simply take the derivative of each component with respect to t of $\boldsymbol{r}(t)$. $\boldsymbol{r'}(t)=\frac{d}{dt}\boldsymbol{a}+\frac{d}{dt}t\boldsymbol{b}+t^2\boldsymbol{c}=0\boldsymbol{a}+\boldsymbol{b}+2t\boldsymbol{c}$
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