Newton_Raphson_method_in_matlab_without_'syms x'

Newton Raphson method code for matlab without 'syms x'

This Code is written without  'syms x'. This logic is applicable in any other language and compiler.
The Script Provides a demonstration of the "Newton - Raphson Method" , to solve various polynomial and transcendental equation. 
Important feature added: You don't need to do the differentiation manually.  Code to find the derivative value is implemented.

Source Code:
clc; clear all; close all;
f=@(x) (x*2.71828^x - cos(x));
x0=input ('x0=');
tol=0.0000001;
N=100;
sqrteps = sqrt(eps);
x(1)=x0;
for n=1:N+1
    h=sqrteps;  
    fp=((f(x(n)+h)-f(x(n)-h))./(2*h));
    if fp==0
        fprintf('derivative=0')
        break
    end
    x(n+1)=x(n)-f(x(n))/fp;
    if abs(x(n+1)-x(n))<=tol
        final1=x(n+1);
        break
    end
end
fprintf('\nThe root of the equation is=%0.5f \n No of Iteration=%d',final1,n)


Input Output:
x0=1
The root of the equation is=0.51776
 No of Iteration=5>>