Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 400: 16


$$y' = 4x^3cos^2(x^4)$$

Work Step by Step

$$y = \int\limits^{x^4}_0 {cos^2\theta} d\theta$$ Using FTC 1, substitute in the upper bound for $\theta$ and multiply the derivative of the upper bound(chain rule). $$y'= cos^2(x^4) \times (x^4)'$$ Simplify. $$y'= cos^2(x^4) \times 4x^3$$ $$y' = 4x^3cos^2(x^4)$$
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