what is the true value of f’(xi ) at xi =𝟏? (use basic calculus) in matlab

To find the true value of f'(xi) at xi = 1 using basic calculus in MATLAB, you need to follow these steps:

1. Define the function f(x) that you want to differentiate.
2. Calculate the derivative of f(x) using MATLAB's symbolic toolbox.
3. Substitute xi = 1 into the derivative expression to find the value of f'(xi) at xi = 1.

Here's a MATLAB code snippet that demonstrates this process:

main.m
syms x;                   % Define x as a symbolic variable
f = sin(x);               % Define the function you want to differentiate

df = diff(f, x);          % Calculate the derivative of f(x)
true_value = subs(df, x, 1);   % Substitute xi = 1 into the derivative expression
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The variable true_value will contain the true value of f'(xi) at xi = 1.

Note: Make sure you have the Symbolic Math Toolbox installed in MATLAB for this code to work.