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: 3


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

Work Step by Step

Usin the product rule: $(uv)'=uv'+u'v $ and using the chain rule: $(f(g(x)))^{\prime}=f^{\prime}(g(x)) g^{\prime}(x)$, we get $$\frac{d}{dx}(x^2y^3)=y^3\frac{d}{dx}(x^2)+x^2\frac{d}{dx}(y^3)\\=2xy^3+3x^2y^2\frac{dy}{dx}.$$
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