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: 12



Work Step by Step

Differentiating with respect to $ x $, we have $1\times y^{2}+2yy'\times x+2xy^{5}+x^{2}5y^{4}y'-3x^{2}=0$ $\implies 2xyy'+x^{2}5y^{4}y'=3x^{2}-y^{2}-2xy^{5}$ $\implies y'=\frac{3x^{2}-y^{2}-2xy^{5}}{2xy+x^{2}5y^{4}}$
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