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: 17


$ y'=\frac{9}{4}x^{\frac{1}{2}}y^{\frac{5}{3}}$

Work Step by Step

Differentiating implicitly with respect to $ x $, we have $-\frac{2}{3}y^{-\frac{5}{3}}y'+\frac{3}{2}x^{\frac{1}{2}}=0$ $-\frac{2}{3}y^{-\frac{5}{3}}y'=-\frac{3}{2}x^{\frac{1}{2}}$ $\implies y'=-\frac{3}{2}x^{\frac{1}{2}}\times-\frac{3}{2}y^{\frac{5}{3}}$ $=\frac{9}{4}x^{\frac{1}{2}}y^{\frac{5}{3}}$
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