Thomas' Calculus 13th Edition

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

Chapter 3: Derivatives - Section 3.1 - Tangents and the Derivative at a Point - Exercises 3.1 - Page 109: 31

Answer

$\frac{dA}{dr}$= 6$\pi$

Work Step by Step

A=$\pi$$r^{2}$ Differentiate with respect to radius to find rate of change of each variable: $\frac{d}{dr}$(A=$\pi$$r^{2})$= $\frac{dA}{dr}$=2*($\pi$$r^{2-1}$)*$\frac{dr}{dr}$ Plug in known values (r=3, $\frac{dr}{dr}$=1) $\frac{dA}{dr}$=2$\pi$(3)(1)= 6$\pi$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.