  We discuss the systematics of obtaining the Callan-Symanzik equation within
the framework of the gauge/gravity dualities. We present a completely general
formula which in particular takes into account the new holographic
renormalization results of arXiv:1102.2239. Non-trivial beta functions are
obtained from new logarithmic terms in the radial expansion of the fields. The
appearance of multi-trace counterterms is also discussed in detail and we show
that mixing between single- and multi-trace operators leads to very specific
non-linearities in the Callan-Symanzik equation. Additionally, we compute the
conformal anomaly for a scalar three-point function in a CFT.
