create a symbolic variable x and use it to define f=(1-x^3)/(1-x)-x^2-1. simplify it using matlab. compute the derivative of f, store in a variable df and the simplify it in matlab

To create a symbolic variable x in MATLAB and define f with its expression, you can use the symbolic math toolbox. Here's how you can do it:

main.m
syms x
f = (1-x^3)/(1-x)-x^2-1;
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To simplify the expression f, you can use the simplify function:

main.m
f_simplified = simplify(f);
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To compute the derivative of f with respect to x, you can use the diff function:

main.m
df = diff(f, x);
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And to simplify the expression df, you can again use the simplify function:

main.m
df_simplified = simplify(df);
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Now, f_simplified will contain the simplified form of f, and df_simplified will contain the simplified form of its derivative df.

Note that the use of the simplify function is optional, but it can help in obtaining a more concise and readable expression.