I'm working through Rasmussen's Gaussian Processes book, and I have a question about the possibility of optimizing additional basis function hyperparameters (in section 2.7 http://www.gaussianprocess.org/gpml/chapters/RW2.pdf). The text explains that the hyperparameters can be varied to maximize the log marginal likelihood, which is given in eq. 2.44 and 2.45. The derivative for the general case is given in eq. 5.9.
I've looked in the gpml code that goes with the book and relevant literature, but I haven't been able to find the derivative wrt the hyperparameters including the basis function hyperparameters.
In other words, for anyone familiar with Gaussian Process Regression, what is the derivative of eq. 2.44 wrt the hyperprior? (again, GPR Book, Ch. 2).