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Compute the partial derivative numerically

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F.O
F.O on 21 Dec 2017
Edited: F.O on 21 Dec 2017
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))

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Accepted Answer

Star Strider
Star Strider on 21 Dec 2017
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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Star Strider
Star Strider on 21 Dec 2017
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.

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