The classical Schwarz-Pick inequality provides a bound for the modulus of the first derivative of an analytic function with norm bounded by 1 on the unit disk. Stefan Ruscheweyh generalized this, obtaining best possible bounds for higher order derivatives. Others have extended these results to various multivariable contexts. Here I discuss work with Milne Anderson and Jim Rovnyak where we use transfer function techniques to obtain such higher order estimates for contractive elements of the multiplier algebra of the Drury-Arveson space. I will also touch on similar results for the polydisk, along with some more recent developments.