Partial Derivatives & the Gradient · Challenge problem

Let $f(x,y) = \dfrac{x^3 - y^3}{x^2 + y^2}$ for $(x,y) \ne (0,0)$ and $f(0,0) = 0$. Using the limit definition, find the directional derivative $D_{\mathbf{u}}f(0,0)$ for $\mathbf{u} = \left(\dfrac{3}{5}, \dfrac{4}{5}\right)$.