how to find derivative at (x,y) in matlab

In MATLAB, you can use the diff function to find the derivative of a function at a specific point.

Here’s an example:

main.m
syms x y
f = x^2 + y^2;
df_dx = diff(f,x)
df_dy = diff(f,y)

x0 = 1; % point of interest
y0 = 2;
df_dx_value = double(subs(df_dx, [x, y], [x0, y0]))
df_dy_value = double(subs(df_dy, [x, y], [x0, y0]))
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In this example, we first define a symbolic function f with variables x and y. We then use the diff function to find the partial derivative of f with respect to x and y.

Next, we define the point of interest (x0, y0). We then use the subs function to substitute x with x0 and y with y0 in the symbolic expressions df_dx and df_dy. Finally, we use the double function to convert the result to a numerical value.

The variables df_dx_value and df_dy_value now contain the values of the partial derivatives of f with respect to x and y, evaluated at the point (x0, y0), respectively.