I am reading a paper by J. Polchinski, called "What is string theory", hep-th/9411028v1. In eq. 1.1.9, and the line before it, the author seems to have used:

$<\partial_z \partial_{\bar{z}} X(z,\bar{z}) X(z',\bar{z}')> = \partial_z \partial_{\bar{z}} <X(z,\bar{z}) X(z',\bar{z}')>$

where the symbol $<F(X)>$ denotes the expected value of $F(X)$ with respect to the "measure" $exp(-S) [dX]$. In other words,

$<F(X)> = \int [dX] exp(-S) F(X)$

(it is a path integral). My question is, why can one pull out the partial derivatives $\partial_z$ and $\partial_{\bar{z}}$ outside the path integral? Or did I missunderstand something? Can someone please give an argument for this, or explain what the author meant perhaps (in case I missunderstood)?