Hello,

I need to find the first and second derivatives of a family of functions. I have to solve in x an ecuation with two parameters
F(x,l,k)=0) to get the functions values.
I´ve tried with Chebyshev approximation and it´s fast but the derivatives oscilate at the extremes of the interval of definition (specialy the second one).
The I went into the dfridr (numerical derivative). I´ve got nice results but it´s difficult to adjust the h parameter for all the functions over the whole interval and it takes a bit too much time to compute the second derivative.
I´m going to try with piecewise polinomical approximation but I need a smooth second derivative. Should I try, splines higher than cubic, Chebyshev, or what?

Thank you

Andrés