So not quite sure what you're missing, but here's how you go about doing this sort of thing.
So first, I am assuming this is 1D due to your description. Second, I'm assuming you know the relationship between points in the physical domain, $x$, and the computational domain, $\xi$, something along the lines of $x=x(\xi)$. Given you have this relationship, you can do the following for some function $\phi(\cdot)$:
$$\begin{align}
\frac{\partial \phi}{\partial x} &= \frac{\partial \phi}{\partial \xi} \frac{\partial \xi}{\partial x}\\
\frac{\partial \phi}{\partial x} &= \frac{\partial \phi}{\partial \xi} \left(\frac{\partial x}{\partial \xi}\right)^{-1}\\
\end{align}$$
With this representation, since you know $x(\xi)$, you can produce the second term exactly in the multiplication. So now you just need to approximate the first term, $\frac{\partial \phi}{\partial \xi}$. This term can be approximated using normal finite difference schemes. Using a central difference, for example, you could get the following:
$$\frac{\partial \phi}{\partial x} = \left(\frac{\phi_{i+1}-\phi_{i-1}}{2\Delta \xi}\right) \left(\frac{\partial x}{\partial \xi}\right)^{-1}$$
In this case, $\phi_{i}$ is associated to both $x_i$ and $\xi_i$, where $\phi_i = \phi(x_i)$, and where, in addition, $\phi_i = \phi(x(\xi_i))$. This should help you understand how to compute the necessary quantity you're after.