Calculus 8th Edition

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

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 140: 16


$S'(R)= 8\pi R$

Work Step by Step

$S(R)=4\pi R^{2}$ by the formulas $(x^{n})'=nx^{n-1}$, $(cf)' = cf'$ $S'(R)=(4\pi R^{2})' = 4\pi (R^{2})'$ lets choose $n=2$ So, $(R^{2})' = nR^{n-1} = 2R^{2-1} = 2R$ therefore $S'(R)=(4\pi R^{2})' = 4\pi (R^{2})'= 4\pi \times 2R = 8\pi R$
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