Answer
$$ y'= 27x(2+9x^2)^{1/2} .$$
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
$$ y'=\frac{3}{2}(2+9x^2)^{1/2}(18x)=27x(2+9x^2)^{1/2} .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - Chapter Review Exercises - Page 163: 35
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