Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 106

Answer

$\frac{dA}{ds} = 12$ $cm$

Work Step by Step

The exercise is asking for the rate of change for area $A$ with respect to its sides $s$. Therefore, it's simply asking us for the first derivative of the function $A$: $$A=s^{2}$$ $$(\frac{d}{ds})A = s^{2} (\frac{d}{ds})$$ $$\frac{dA}{ds} = 2s^{2-1} = 2s$$. For the value $s = 6cm$: $$\frac{dA}{ds} = 2(6) = 12 cm$$
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