# Derivative of an integral

• Sep 10th 2011, 07:12 AM
flybynight
Derivative of an integral
Hey guys,
I am looking at this problem, and I don't have any idea how to do it: $\frac{d}{dx}\int_x^3e^{{-t}^2}dt$

Any help would be greatly appreciated.
Thanks,
Peter
• Sep 10th 2011, 07:25 AM
Plato
Re: Derivative of an integral
Quote:

Originally Posted by flybynight
Hey guys,
I am looking at this problem, and I don't have any idea how to do it: $\frac{d}{dx}\int_x^3e^{{-t}^2}dt$

Suppose that each of $g~\&~h$ is s differentiable function then
$\frac{d}{{dx}}\int_{h(x)}^{g(x)} {f(t)dt} = g'(x)f(g(x)) - h'(x)f(h(x))$.