Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.3 Partial Derivatives - 14.3 Exercises - Page 967: 95


$\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$

Work Step by Step

$ \dfrac{\partial K}{\partial m}=\dfrac{\partial}{\partial m}[\dfrac{1}{2}mv^{2}]=\dfrac{1}{2}v^{2}$ ...(1) $\dfrac{\partial K}{\partial v}=\dfrac{\partial}{\partial v}[(\dfrac{1}{2})mv^{2}]=mv$ ...(2) From the equations (1) and (2), we have $ \dfrac{\partial^{2}K}{\partial v^{2}}=\dfrac{\partial}{\partial v}[mv]=m$ and $\dfrac{\partial K}{\partial m}\times\dfrac{\partial^{2}K}{\partial v^{2}}=\dfrac{1}{2} \times (mv^{2})=K$ After solving, we get $\dfrac{\partial K}{\partial m}\dfrac{\partial^{2}K}{\partial v^{2}}=K$
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.