Problem in evaluating the value of the derivative of multivariable function

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I'm triyng to make a function that uses the Newton - Raphson method to solve a system of 2 equation

function [x_final, y_final, f1_final, f2_final, iter, errs, arrs] = Sys_equa_newton(f1, f2, x0, y0, err, max_iter)
    %newton_sys - Description
    %
    % Syntax: y = newton_sys(input)
    %
    % Long description
    % f1: first funtion of 2 variables
    % f2: second funtion of 2 variables
    % x0: initial value of x
    % y0: initial value of y
    % err: threshold value of error to stop
    % max_iter: maximum iteration to stop
    cur_err = 1;
    iter = 0;
    syms x y;
    df1_x = matlabFunction(diff(f1, x));
    df1_y = matlabFunction(diff(f1, y));
    df2_x = matlabFunction(diff(f2, x));
    df2_y = matlabFunction(diff(f2, y));
    x = x0;
    y = y0;
    X_n = f1(x, y) * (df2_y(x, y)) - f2(x, y) * (df1_y(x, y));
    Y_n = f2(x, y) * (df1_x(x, y)) - f1(x, y) * (df2_x(x, y));
    Deno = df1_x(x, y) * df2_y(x, y) - df1_y(x, y) * df2_x(x, y);
    arrs = zeros(2,max_iter);
    errs = zeros(2,max_iter);
    while ((cur_err > err) && (iter <= max_iter))
        x_old = x;
        x = x_old - X_n / Deno;
        y_old = y;
        y = y_old - Y_n / Deno;
        err_x = abs(x - x_old) / x;
        err_y = abs(y - y_old) / y;
        arrs(:,iter+1) = [x; y];
        errs(:,iter+1) = [err_x; err_y];
        iter = iter+1;
        cur_err = err_x + err_y;
    end
    x_final = x;
    y_final = y;
    f1_final = f1(x_final,y_final);
    f2_final = f2(x_final,y_final);
end

But if I enter a function that only has the first power of x or y or both x and y are in first power, when i calculate the derivatrive (df1_x for example) then the new function only have 1 argument or 0 argument if both x and y are in first power.

So is there anyway to solve this problem, I'm trying to make a general function that can work with all 2 system of equation