create a function that will perform newton's method without the user inputting the derivative in matlab

To create a function that performs Newton's method without the user inputting the derivative in MATLAB, you can use the diff function to automatically compute the derivative of the function numerically. Here is an example of how to implement the function:

main.m
function [root, iterations] = newtonsMethod(func, x0, tol, maxIter)
    % Initialize variables
    iterations = 0;
    diffFunc = diff(func); % Compute the derivative of the function
    
    % Perform Newton's method
    while true
        x1 = x0 - func(x0) / diffFunc(x0); % Compute the next approximation using the derivative
        iterations = iterations + 1;
        
        % Check stopping conditions
        if abs(x1 - x0) < tol || iterations >= maxIter
            break;
        end
        
        x0 = x1; % Update the current approximation
    end
    
    root = x1; % Store the final root
end
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In this code, func is the function for which we want to find the root, x0 is the initial guess, tol is the tolerance for convergence, and maxIter is the maximum number of iterations allowed. The function diff(func) computes the derivative of func using MATLAB's symbolic differentiation capabilities.

You can call this function with your desired function, initial guess, tolerance, and maximum number of iterations. It will return the estimated root and the number of iterations performed.

Note that this code assumes that the input function func is defined using MATLAB's symbolic math toolbox or as an anonymous function.