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

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

$$y = \int\limits^{x^4}_0 {cos^2\theta} d\theta$$ 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. $$y'= cos^2(x^4) \times 4x^3$$ $$y' = 4x^3cos^2(x^4)$$