MATLAB: Compute the partial derivative numerically

MATLABpartial derivative

Hi, I want to compute the first and second partial derivative with respect to x, y for this function
x0=0
y0=0
x=[-1:0.1:1];
y=[-2:0.1:2];
v=x+exp(-((x-x0).^2+(y-y0).^2))

Best Answer

See if the gradient (link) function will do what you want:
Example —
x0=0;
y0=0;
x=[-1:0.1:1];
y=[-2:0.1:2];
[X,Y] = meshgrid(x, y);
v = @(x,y) x+exp(-((x-x0).^2+(y-y0).^2));
[dX,dY] = gradient(v(X,Y));
figure(1)
surf(X, Y, v(X,Y), 'FaceAlpha',0.5, 'EdgeColor',[0.3 0.3 0.7])
hold on
surf(X, Y, dX, 'EdgeColor','g')
surf(X, Y, dY, 'EdgeColor','r')
hold off
grid on
legend('v(x,y)', 'dX', 'dY')
xlabel('\bfX')
ylabel('\bfY')
view(40, 20)
figure(2)
contour(X, Y, v(X,Y))
hold on
quiver(X, Y, dX, dY)
hold off
legend('v(x,y)', 'Gradient')
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