Newtons Divided Difference First Derivative

[NotASmurf]

Hey all, for a function approximation program t run fast enough i need to solve for where the function (represented by a NDDP) is at a minimum (necessary trust me), althogh I have no idea how to go about differentiating it, i tried to break it up from its's general formula (the pi operators and the sigma summations make the differentiation difficult for me as i have never had to differentiate a pi operator before), but that seems to make things worst is the first derivative for a nth order NDDP known? Any help apreciated.

 

[BvU]

2.2 here perhaps ? Or did you find that already ?

 

[NotASmurf]

Thanks :D

 

[NotASmurf]

Wasnt familiar with the reccurance relation version so that paper didn't help too much, however found a nice pattern, turns out the derivative is

$$ \sum_{k=0}^{k<=n}\sum_{i=0}^{k} \Pi_{j=0, j \neq i}^{k-1} (x-x_j) $$

You can see it in action here for 4th order poly