Math Help - Leibnez Rule

Hi all, I have to solve the following problem:

Find dV/dt, where:

where F(x) is the cdf of x on [0, ) and f(x) is its corresponding pdf.

My question is can I just use Leibnez rule as one normally would, or does the whole cdf thing complicate matters? My senses tell me its the former.

If "F(x) is the cdf of x on [0,) and f(x) is its corresponding pdf" then so the integral is
and its derivative, by the Leibniz rule, is simply .