Consider two arbitrary sets of coordinates $z_0$ and $z$ in some space, mapped via some $\bar{z} :$=$z_0 \rightarrow z$
I have a function $$\tag{1}\rho(z)=\int\delta(z-\bar{z}(z_0))\rho_0 (z_0)dz_0$$ this will give me $$\tag{2}\rho(z)=\rho_0 (\bar{z}^{-1}(z))\frac{\partial z_0}{\partial z}$$ How to obtain equation (2) from equation (1).
