Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 163: 35


$$ y'= 27x(2+9x^2)^{1/2} .$$

Work Step by Step

Recall that $(x^n)'=nx^{n-1}$ Since $ y=(2+9x^2)^{3/2}$, then by the chain rule the derivative $ y'$ is given by $$ y'=\frac{3}{2}(2+9x^2)^{1/2}(18x)=27x(2+9x^2)^{1/2} .$$
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