Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises - Page 181: 53


a) V = $\frac{5.3}{P}$ b) V' = -2.12x$10^{-3}$ $\frac{m^{3}}{kPa}$

Work Step by Step

a) PV = k, where k is constant (the question says that the pressure P is inversely proportional to the value V of the gas) 0.106$\times$50 = k, k = 5.3 V = $\frac{5.3}{P}$ b) V = $\frac{5.3}{P}$, P = 50kPa V' = 5.3$P^{-1}$ bring P to the numerator V' = -5.3$P^{-2}$ use power rule V' = $\frac{-5.3}{P^{2}}$ V' = $\frac{-5.3}{50^{2}}$ = -2.12x$10^{-3}$ $\frac{m^{3}}{kPa}$
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