Deriving the Fisher $z$-transformation from the delta method

For a sample correlation coefficient r, it is known that $\sqrt n(r-\rho)\overset{d}{\longrightarrow} N(0,(1-\rho^2)^2)$, where $\rho$ is the population correlation coefficient. For what transformation $g(.)$, $\sqrt n(g(r)-g(\rho))\overset{d}{\longrightarrow} N(0,1)$?