A contour plot of f ( x , y ) = x 2 + y 2 {\displaystyle f(x,y)=x^{2}+y^{2}} , showing the gradient vector in black, and the unit vector u {\displaystyle \mathbf {u} } scaled by the directional derivative in the direction of u {\displaystyle \mathbf {u} } in orange. The gradient vector is longer because the gradient points in the direction of greatest rate of increase of a function.