The question:

Find F'(x) for the function F:R -> R given below:

$\displaystyle F(x) = \int^{x^3}_0 {sin(t^2)dt$

My attempt:

It is my understanding that the First Fundamental Theorem of Calculus states that:

F'(x) = f(x)

So my solution was just $\displaystyle sin(x^2)$. However, this isn't the correct solution. I'm not sure what I'm doing wrong. Any assistance would be appreciated. Thanks.