Update (16 Dec): The B-spline derivative code made it into GSL's 1.12 release
I'm trying to get B-spline derivative capabilities added to gsl. Though I could find lots of implementations of B-spline derivatives for fixed polynomial order, finding derivatives for arbitrary order B-splines turns out to be a gap in many libraries (with PPPACK being the notable exception).
It also turns out that finding a good, concrete verification test case is a pain too. Hopefully gsl will pick up my patch and no one will have to implement these again. But, if you should find yourself in that situation, here's some Mathematica that provides both symbolic and numeric results for quadratic B-splines and their derivatives on a particular set of knots:A verification case for B-Spline implementations, including derivatives