Editing B-spline (section)

==Derivative expressions==
The derivative of a B-spline of degree ''k'' is simply a function of B-splines of degree ''k''&nbsp;−&nbsp;1:<ref>de Boor, p. 115.</ref>
:<math>\frac{dB_{i,k}(x)}{dx} = k\left(\frac{B_{i,k-1}(x)}{t_{i+k} - t_i} - \frac{B_{i+1,k-1}(x)}{t_{i+k+1} - t_{i+1}}\right).</math>
This implies that
:<math>\frac{d}{dx} \sum_i \alpha_i B_{i,k} = \sum_{i=r-k+2}^{s-1} k\frac{\alpha_i - \alpha_{i-1}}{t_{i+k} - t_i}B_{i,k-1} \quad \text{on} \quad [t_r, t_s],</math>
which shows that there is a simple relationship between the derivative of a spline function and the B-splines of degree one less.