diffrentiation solver in matlab

MATLAB provides a diff function to differentiate a given function or set of data points. The syntax of this function is as follows:

main.m
dydx = diff(y) ./ diff(x)
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where y is the vector of function values and x is the corresponding vector of independent variable values. The output dydx contains the numerical values of the derivative.

Alternatively, if you have a symbolic expression of the function, you can use the diff function from the Symbolic Math Toolbox to calculate the derivative symbolically. The syntax is as follows:

main.m
syms x
f = x^2 + 2*x + 1;
dfdx = diff(f, x)
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Here, we define a symbolic expression f, and then use the diff function to calculate its derivative with respect to x. The output dfdx is another symbolic expression, which can be simplified with the simplify function.

main.m
dfdx = simplify(dfdx)
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This will simplify the expression to (2*x + 2).

Note that diff can also be used to perform higher-order differentiations by specifying the differentiation order as a second argument. For example, to calculate the second derivative of a function f, you can use:

main.m
d2fdx2 = diff(f, x, 2)
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