Atop Mathematica 126.96.36.199 I see incorrect ComplexInfinity's arise when evaluating the derivatives of BSplineBasis functions.
Run the following snippet
and observe that the first and last entry of the table are ComplexInfinity. BSplineBasis should allow symbolic differentiation of the first and last basis function for a given set of knots.
[This was corrected in 8.0 - Forum Moderator]