suppose f(x) = exp(x), and we want to find f’(x) at xi =1. what is the true value of f’(xi ) at xi =𝟏? in matlab

To find the true value of f'(x) at xi = 1 for the function f(x) = exp(x) in MATLAB, you can use symbolic differentiation. Here's how you can do it:

main.m
syms x;
f = exp(x);
df = diff(f, x);
xi = 1;
f_prime_xi = subs(df, x, xi);
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Explanation:

• We start by declaring the symbolic variable x using the syms function in MATLAB.
• Next, we define the function f(x) = exp(x) using the exp function.
• Then, we use the diff function to differentiate f(x) with respect to x, which will give us the derivative f'(x).
• After that, we assign a value of xi = 1.
• Finally, we substitute the value of xi in the derivative expression using the subs function, which will give us the true value of f'(xi).

The variable f_prime_xi will contain the true value of f'(xi) at xi = 1.

Note: The result will be an exact value since we used symbolic differentiation.

Please make sure you have the Symbolic Math Toolbox installed in MATLAB to perform symbolic computations.