Compute the partial derivative numerically

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))

Answer 1

[Star Strider]

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')

[F.O]

and i f i want the second derivative then i just write ?????

[dXX,dYY]=gradient(gradient (v(x,y))

[Star Strider]

The easiest way is to use the related del2 (link) function. Remember to multiply it by 4 to get the second derivative:

d2Z = 4*del2(v(X,Y));

referencing my earlier code for the function call. See the del2 documentation for details, since it works a bit differently than gradient.

[F.O]

Thanks for the answer

[Star Strider]

My pleasure.