Finding the derivative from an intergral.

**ebonyscythe** · November 29th 2007, 04:51 AM

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.

**galactus** · November 29th 2007, 05:05 AM

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

What I am trying to say is:

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

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