Comparing the first second and fourth order approximations of the first derivative against the analytical or exact derivative

Objective: close all clear all clc % given conditions x = pi/3; % assume range of dx dx = linspace(pi/4,pi/4000,20); % given F(x) = sin(x)/x^3 % first derivative F\'(x) = (cos(x)*x^3 - 3*x^2*sin(x))/x^6 analytical_derivative = (cos(x)*x^3 - 3*x^2*sin(x))/x^6; for i = 1:length(dx) % first order approximation error…