Numerical discretization

Objective: Program coding: clear all close all x=pi/3; dx=1/40; analytical_function=sin(x)/x^3; analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; first_order_approx=(((sin(x+dx))/((x+dx)^3))-((sin(x)/x^3)))/(dx); second_order_approx=(((sin(x+dx))/((x+dx)^3))-((sin(x-dx))/(x-dx)^3))/(2*dx); fourth_order_approx=((sin(x-2*dx)/(x-2*dx)^3)-(8*sin(x-dx)/(x-dx)^3)+(8*sin(x+dx)/(x+dx)^3)-(sin(x+2*dx)/(x+2*dx)^3))/(12*dx);…