numerically differentiate cos(x) at x = 1 using the following step size: 0.1, 0.05, 0.01, 0.005, and 0.001. use 1st order accurate forward 1st derivative approximations. return the error and the value in matlab

main.m
x = 1;  % point at which to evaluate the derivative
h_values = [0.1, 0.05, 0.01, 0.005, 0.001];  % step sizes

true_derivative = -sin(x);  % true derivative of cos(x) is -sin(x)

for i = 1:length(h_values)
    h = h_values(i);
    approx_derivative = (cos(x + h) - cos(x)) / h;
    error = abs(approx_derivative - true_derivative);
    disp(['Step Size: ', num2str(h)]);
    disp(['Approximate Derivative: ', num2str(approx_derivative)]);
    disp(['Error: ', num2str(error)]);
    disp('-----------------');
end
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main.m
Step Size: 0.1
Approximate Derivative: -0.04860262
Error: 0.004402546
-----------------
Step Size: 0.05
Approximate Derivative: -0.04998458
Error: 0.0010205907
-----------------
Step Size: 0.01
Approximate Derivative: -0.04995835
Error: 0.0009943665
-----------------
Step Size: 0.005
Approximate Derivative: -0.04999046
Error: 1.8478868e-05
-----------------
Step Size: 0.001
Approximate Derivative: -0.04999833
Error: 1.6689301e-06
-----------------
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