Partial Derivatives & the Gradient · Superchallenge problem

Let $R(x,y,z) = \dfrac{x^2 + 2y^2 + 3z^2}{x^2 + y^2 + z^2}$ for $(x,y,z) \ne (0,0,0)$. Find the largest value of $\lvert\nabla R\rvert$ over all points of the unit sphere $x^2 + y^2 + z^2 = 1$.