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: 5


$$\frac{d}{dx}(x^2+y^2)^{3/2}= 3(x+y\frac{dy}{dx})(x^2+y^2)^{1/2} .$$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Using the chain rule, we have $$\frac{d}{dx}(x^2+y^2)^{3/2}= \frac{3}{2}(x^2+y^2)^{1/2}(2x+2y\frac{dy}{dx})=3(x+y\frac{dy}{dx})(x^2+y^2)^{1/2} .$$
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