calculate the first derivative of the function using the backward difference approximation method in matlab

To calculate the first derivative of a function using the backward difference approximation method in MATLAB, you can use the following code:

main.m
function df = backward_diff(f, x, h)
% BACKWARD_DIFF calculates the first derivative of the function using the backward difference approximation method
%
%   df = BACKWARD_DIFF(f, x, h) calculates the first derivative of the function f at the point x using
%   the backward difference approximation method with step size h.

df = (f(x) - f(x-h)) / h;
end
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In this code, the backward_diff function takes in three parameters: f, the function to differentiate, x, the point at which to calculate the derivative, and h, the step size to use in the backward difference approximation.

The backward difference approximation calculates the first derivative by taking the difference between f(x) and f(x-h), and dividing that by h. This gives an approximation of the derivative of f at x.

To use this function, simply pass in your function f, the value of x at which to calculate the derivative, and the desired step size h. For example, to calculate the derivative of sin(x) at x = pi/4 using a step size of 0.1, you would call the function like this:

main.m
f = @(x) sin(x);
x = pi/4;
h = 0.1;

df = backward_diff(f, x, h);
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The resulting value of df would be an approximation of the first derivative of sin(x) at x = pi/4 using the backward difference approximation method.