Solution
= Solution
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. Therefore
$$
\boxed{\hat{\mathbf n}_{\rm increase}=\frac{(1,2)}{\sqrt5},\qquad |\nabla T|=\frac2{\sqrt5}.}
$$
The direction is radially outward from the origin, perpendicular to the circular <level curve> through the point.