Fundamental Theorem of Calculus question

Question

Find G'(x) by using the Fundamental Theorem of Calculus.

Answer 1

By Fundamental Theorem of Calculus

G'=d/dx(∫sin^5tdt) where ∫ is from (x^2-5) to (1/x)

First you calculate:

∫sin^5dt (where ∫ is from (x^2-5) to 1/x) which will give you a function with variable x

Then you calculate the derivative with respect to x

Answer 2

G'(x) = sin⁵(1/x)(1/x)' - sin⁵(x² - 5)(x² - 5)' = -1/x²·sin⁵(1/x) - 2x·sin⁵(x² - 5)