Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 11


$y'' = 12\theta + 14$ $y'''= 12$

Work Step by Step

First, we can distribute the $\theta^2$ to simplify the problem: $y = 2\theta^3 + 7\theta^2$ To find the second derivative, you need to find the first derivative first, so we differentiate the equation using the power rule: $y' = 6\theta^2 + 14\theta$ Then we find the derivative of $y'$ to find $y''$ using the power rule: $y'' = 12\theta + 14$ Finally, to find $y'''$, we find the derivative of $y''$ as follows: $y'''= 12$
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