Past exam of the mathematical methods II course of the University of Oxford / 2013 / 4 / a

The gradient is $\nabla T=2(x,y)/(x^2+y^2)$ and at $(1,2)$ it is $(2/5,4/5)$. The directional derivative along a unit vector is maximal in the gradient direction. ThereforeThe direction is radially outward from the origin, perpendicular to the circular level curve through the point.