# Thread: Derivative of an integral

1. ## Derivative of an integral

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

Any help would be greatly appreciated.
Thanks,
Peter

2. ## Re: Derivative of an integral

Originally Posted by flybynight
Hey guys,
I am looking at this problem, and I don't have any idea how to do it: $\displaystyle \frac{d}{dx}\int_x^3e^{{-t}^2}dt$
Suppose that each of $\displaystyle g~\&~h$ is s differentiable function then
$\displaystyle \frac{d}{{dx}}\int_{h(x)}^{g(x)} {f(t)dt} = g'(x)f(g(x)) - h'(x)f(h(x))$.