# Thread: Apply the Fundemental Theorem of Calculus to find the Derivative

1. ## Apply the Fundemental Theorem of Calculus to find the Derivative

2. $F(x) = \int_2^x \sqrt{t-1} dt$ then $F(x^2) = \int_2^{x^2} \sqrt{t-1}dt$. Thus, $[F(x^2)]' = 2xF'(x^2) = 2x\sqrt{x^2-1}$.