This plot shows the gradient, j^{\displaystyle {\hat {j}}}, and j^{\displaystyle {\hat {j}}} scaled by the directional derivative in the direction of j^{\displaystyle {\hat {j}}} of f(x,y)=x2+y2{\displaystyle f(x,y)=x^{2}+y^{2}} at (−5, 5).
Created with the following Sage code, and later edited in Inkscape:

(contour_plot(x^2 + y^2, (x, -20, 0), (y, 0, 20), contours=range(50, 850, 50), cmap='summer') + point((-5, 5), color='red', size=15, zorder=4) +
arrow([-5, 5], [-15, 15], zorder=2) + arrow([-5, 5], [-5, 15], zorder=2, color='darkorange') + arrow([-5, 5], [-5, 6], zorder=3, color='darkgreen') +
text(r'$\nabla_\mathbf{u} f(-5, 5)$', (-12.5, 9.5), fontsize=14) + text(r'$\mathbf{u}$', (-4.3, 5.5), color='darkgreen', fontsize=14) +
text(r'$\mathbf{u}\nabla_\mathbf{u} f(-5, 5)$', (-2.3, 11.5), color='darkorange', fontsize=14))
Own work
Eviatar Bach