Partial Derivatives & the Gradient · Superchallenge problem

Let $f(x,y) = \dfrac{x^2y}{x^2 + y^2}$ for $(x,y) \ne (0,0)$ and $f(0,0) = 0$. For each unit vector $\mathbf{u}$ the directional derivative $D_{\mathbf{u}}f(0,0) = \displaystyle\lim_{h\to 0}\frac{f(h\mathbf{u}) - f(0,0)}{h}$ exists. Find the largest value of $D_{\mathbf{u}}f(0,0)$ over all unit vectors $\mathbf{u}$.