I'm being asked to calculate, explicitly the following derivative:

$$
\frac{d}{d x}\left[\int\_{e^{-x}}^{e^{x}} \sqrt{1+(\ln t)^{2}} d t\right]
$$

How can I do that?

I thought about using the fundamental theorem of calculus and chain rule but I'm not sure about this approach. I think that the integral itself can not be done analyticalally, so I can not integrate it first to do the derivative latter.