Calculus 8th Edition

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

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises - Page 160: 79

Answer

By the Chain Rule $a(t)$ = $\frac{dv}{dt}$ = $\frac{dv}{ds}{\frac{ds}{dt}}$ = $\frac{dv}{ds}v(t)$ = $v(t)\frac{dv}{ds}$ The derivative $\frac{dv}{dt}$ is the rate of change of the velocity with respect to time (in other words, the acceleration) whereas the derivative $\frac{dv}{ds}$ is the rate of change of the velocity with respect to the displacement.

Work Step by Step

By the Chain Rule $a(t)$ = $\frac{dv}{dt}$ = $\frac{dv}{ds}{\frac{ds}{dt}}$ = $\frac{dv}{ds}v(t)$ = $v(t)\frac{dv}{ds}$ The derivative $\frac{dv}{dt}$ is the rate of change of the velocity with respect to time (in other words, the acceleration) whereas the derivative $\frac{dv}{ds}$ is the rate of change of the velocity with respect to the displacement.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.