# Derivative of B-spline basis functions for degree 2

Lets first derivative of $N_{i,p}(t)$ (i-th Bspline basis function) is as follow:

$N'_{i,p}(t)=\frac{p}{t_{i+p}-t_{i}}N_{i,p-1}(t)+ \frac{p}{t_{i+p+1}-t_{i+1}}N_{i+1,p-1}(t)$

Now Let's consider a bi-infinite knot vector. verify explicitly without resorting to the above-said formula for p=2, if $t_i\ < t < t_{i+1}$

would you please give me hint regarding above simple question! (thank you in advance)

the problem is that the interval is open $]t_i, t_{i+1}[$ .