manually determine the gradient of a function in matlab

To manually determine the gradient of a function in Matlab, you can use the symbolic math toolbox. Here is an example of how to find the gradient of a function using this approach:

1. Define your function as a symbolic expression using the "syms" command. For example:

main.m
syms x y
f = x^2 + y^3;
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2. Use the "gradient" command to compute the gradient of the function. This will return a vector with the partial derivatives of the function with respect to each input variable. For our example, we can compute the gradient as follows:

main.m
grad = gradient(f, [x, y]);
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3. Finally, evaluate the gradient at a specific point by substituting in the values of the input variables. For example, if we want to evaluate the gradient at the point (1,2), we can do the following:

main.m
subs(grad, [x, y], [1, 2]);
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The output of this command will be the gradient of the function at the point (1,2), which is [2, 12].