[Python] B-Spline derivative using de Boor's algorithm

Wikipedia gives us a Python implementation for the de Boor's algorithm:

def deBoor(k, x, t, c, p):
"""
Evaluates S(x).

Args
----
k: index of knot interval that contains x
x: position
t: array of knot positions, needs to be padded as described above
c: array of control points
p: degree of B-spline
"""
d = [c[j + k - p] for j in range(0, p+1)]

for r in range(1, p+1):
for j in range(p, r-1, -1):
alpha = (x - t[j+k-p]) / (t[j+1+k-r] - t[j+k-p])
d[j] = (1.0 - alpha) * d[j-1] + alpha * d[j]

return d[p]


Is there a similar algorithm calculating the derivative of the B-Spline interpolated curve (or even n-th derivative)?

I know that mathematically it is reduced to using a spline of the lower order but can't apply it to the de Boor's algorithm.

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