  It is shown that if a point $x_0$ admits a bounded point derivation on
$R^p(X)$, the closure of rational function with poles off $X$ in the $L^p(dA)$
norm, for $p >2$, then there is an approximate derivative at $x_0$. A similar
result is proven for higher order bounded point derivations. This extends a
result of Wang which was proven for $R(X)$, the uniform closure of rational
functions with poles off $X$.
