Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 50


(a) $-\frac{2}{3}$ (b) $4$

Work Step by Step

(a) $\frac{dI}{dR}= \frac{d}{dR}(\frac{V}{R})=V\frac{d}{dR}(\frac{1}{R})=V\times-\frac{1}{R^{2}}$ As $V=24$, $\frac{dI}{dR}|_{R=6}=24\times-\frac{1}{6^{2}}=-\frac{2}{3}$ (b) $\frac{dV}{dR}=\frac{d}{dR}(IR)=I\frac{dR}{dR}=I\times1=I=4$
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