Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.8 Implicit Differentiation - Exercises - Page 152: 19



Work Step by Step

Differentiating implicitly with respect to $ x $, we have $ y'+\frac{-y'}{y^{2}}=2x+1$ $\implies y'(1-\frac{1}{y^{2}})=2x+1$ $\implies y'=\frac{2x+1}{1-\frac{1}{y^{2}}}$ $\implies y'=\frac{(2x+1)y^{2}}{y^{2}-1}$
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