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 966: 83


$\dfrac{\partial R}{\partial R_{1}}=[\dfrac{R}{R_{1}}]^2$

Work Step by Step

We will have to use $\dfrac{\partial}{\partial R_{1}}$ to both sides of the given equation. Now, we will use chain rule in the LHS equation as R is a function of $R_{1}.$ Consider $R_{2},$ and $R_{3}$ keep treating as constants. $\dfrac{\partial}{\partial R_{1}}[R^{-1}]=\dfrac{\partial}{\partial R_{1}}[R_{1}^{-1}]+0+0$ This implies that $-[R]^{-2}\times \dfrac{\partial R}{\partial R_{1}}=-R_{1}^{-2}$ Thus, we get $\dfrac{\partial R}{\partial R_{1}}=[\dfrac{R}{R_{1}}]^2$
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