Effect of dx on errors of different approximations

Objective: Fourth_order_approx program code function out = fourth_order_approx(x,dx); analytical_derivative=((x^3*cos(x))-(sin(x)*3*x^2))/x^6; fourth_order_equation=((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) out=abs(fourth_order_equation-analytical_derivative); end​ …