Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.3 Differentiation Rules - Exercises 3.3 - Page 126: 60

Answer

$\frac{dR}{dM}=CM-M^2$

Work Step by Step

Step 1. Replace $R$ with $y$, and replace $M$ with $x$; the function can be rewritten as $y=x^2(C/2-x/3)=-x^3/3+Cx^2/2$ where $C$ is a constant. Step 2. Find the derivative: $\frac{dy}{dx}=-x^2+Cx$ Step 3. Changing back to the original symbol, we have $\frac{dR}{dM}=-M^2+CM=CM-M^2$
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