# Math Help - Finding the derivative from an intergral.

1. ## Finding the derivative from an intergral.

I want to make sure I'm doing this right, and if I'm not, what I'm doing wrong. My notes on this section were terrible...

Find the derivative of the following function of x.

$F(x) = \int_2^{x^3}\cos(t^2)dt$

So $F'(x) = \cos(x^4)*2x$ , that's what's in my notes as far as I can tell... not sure why it's not the -sin(x^4) or something. Maybe I just wrote it down wrong.

Any help is appreciated.

2. $\frac{d}{dx}\int_{f(x)}^{g(x)}f(t)dt=g'(x)f(g(x))$

What I am trying to say is:

$\frac{d}{dx}\int_{2}^{x^{3}}cos(t^{2})dt=3x^{2}cos (x^{6})$