% Plot f(x,y) = x e^(-x^2 - y^2) with contours and its gradient as arrows.
x = linspace(-2, 2, 30);
y = linspace(-2, 2, 30);

[X,Y] = meshgrid(x,y);

F = X .* exp(-X.^2 - Y.^2);  % evaluate f(x,y) on mesh
contour(x,y,F);              % draw contour plot of f

% let dfdy = y component of grad F = df/dy

dfdx = (1-2*X.^2) .* exp(-X.^2 - Y.^2); % evaluate dfdx on mesh
dfdy = -2*X.*Y .* exp(-X.^2 - Y.^2);    % evaluate dfdy on mesh

hold on
quiver(x,y,dfdx,dfdy);       % draw quiver plot

xlabel('x')
ylabel('y')
title('f(x,y) = x e^{-x^2 - y^2} with \nabla f arrow plot')
colorbar()