Question

Use the Fundamental Theorem of Calculus to find the derivative of

f(x)=∫[4,x^2]((1/4)t^2−1)^15 dt

Answer 1

that would be

((1/4)(x^2)^2−1)^15 * 2x
= 2x(x^4/4 - 1)^15

Answer 2

To fully understand what Steve did, watch these two KhanAcademy clips
https://www.khanacademy.org/math/ap-calculus-ab/fundamental-theorem-of-calculus-ab/fundamental-theorem-of-calculus-tut-ab/v/fundamental-theorem-of-calculus
and
https://www.khanacademy.org/math/ap-calculus-ab/fundamental-theorem-of-calculus-ab/fundamental-theorem-of-calculus-tut-ab/v/applying-the-fundamental-theorem-of-calculus

special emphasis on the second of those two.