If we assume that we have a given launcher that is able to produce a $\Delta v$ of 10km/s at sea level takeoff, and is able to reach an LEO of 200km above sea level, what LEO altitude would that launcher achieve if if the launchpad was located at an altitude X above sea level? Say 15km above sea level?
I stumbled over this function,
\begin{align} \Delta v = \sqrt {2GM_{\oplus} \left( \frac{1}{r_{\oplus}}- \frac{1}{r_{target}} \right)} \end{align}
which is a solution to the underlying work integral with a lot of simplifications
\begin{align} W = \int \vec F \cdot d\vec s \end{align}
Given $\Delta v$ being constant, with all simplifications I do doubt solving the equation
\begin{align} \sqrt {2GM_{\oplus} \left( \frac{1}{r_{\oplus}}- \frac{1}{r_{target}} \right)} = \sqrt {2GM_{\oplus} \left( \frac{1}{r_{\oplus}+x}- \frac{1}{r_{target}} \right)} \end{align}
towards $r_{target}$
will do the job.