Thomas' Calculus 13th Edition

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

Chapter 3: Derivatives - Practice Exercises - Page 178: 52



Work Step by Step

Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "r" variables since we are differentiating with respect to s: $2r\times1+2s\frac{dr}{ds}-\frac{dr}{ds}-1+2s=0$ $2r+2s\frac{dr}{ds}-\frac{dr}{ds}-1+2s=0$ Move all terms with dr/ds to one side of the equation, and isolate dr/ds: $2s\frac{dr}{ds}-\frac{dr}{ds}=1-2r-2s$ $\frac{dr}{ds}(2s-1)=1-2r-2s$ $\frac{dr}{ds}=\frac{1-2r-2s}{2s-1}$
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