I have proposed to solve this problem but I am already giving up because I cannot find a way out. If someone has come across it and solved it, I appreciate how to face the solution.
I want to estimate the maximum error of interpolation that is made, when trying to approximate the function
$$y=\tan(\sin(x^3))$$
the interpolation polynomial is of degree 6, using Newton's technique of divided differences. And the problem I really have is that I have to calculate the derivative $f^{(8)}$ to determine the absolute maximum of the $f^{(7)}$ and be able to limit this function. But the eighth derivative of this particular function is a BIG equation. Does anyone have any strategies that I can share for this transcendent function?.