centraldifference approximation to the first derivative of a function in matlab

In MATLAB, the central difference approximation to the first derivative of a function f(x) at point x0 can be computed using the following code:

main.m
function df = central_diff(f, x0, h)
% Compute central difference approximation to first derivative of f at x0 using step size h
df = (f(x0 + h) - f(x0 - h)) / (2*h);
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Here, f is a function handle that represents the function f(x), x0 is the point at which to compute the derivative approximation, and h is the step size. The central difference approximation is given by the formula:

To use this function, you can define your function f as a separate MATLAB function or anonymous function, and call the central_diff function with appropriate arguments:

main.m
% Example usage:
f = @(x) sin(x);   % Define function as an anonymous function
x0 = pi/4;         % Point at which to compute derivative
h = 0.001;         % Step size
df = central_diff(f, x0, h);   % Compute derivative approximation
disp(df);          % Display result
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This will compute the central difference approximation to f'(x) at x0 using step size h, and store the result in the variable df. The result can be displayed using the disp function.