I am working through an economics paper and I need to take the derivative of the following function:
$h\left(\overline{\omega}\right) = \int^{\infty}_{\overline{\omega}} \omega \Phi \left(d\omega\right)$
Even though I don't understand it well, I can do the derivative for the case
$g\left(\overline{\omega}\right) = \int^{\overline{\omega}}_{0} \omega \Phi \left(d\omega\right)$
where the derivative is simply
$g'\left(\overline{\omega}\right) = \overline{\omega} \phi \left(\overline{\omega}\right)$
But for $h\left(\overline{\omega}\right)$ where the upper bound is $\infty$ I really have no idea of what to do.
Can anyone help me? Any explanation or even a pointer to where I can learn those things would be greatly appreciated.