Partial Derivatives & the Gradient · Challenge problem

Let $f(x,y) = x^3 + xy^2$ and $\mathbf{u} = \left(\dfrac{3}{5}, \dfrac{4}{5}\right)$. The second directional derivative $D_{\mathbf{u}}^2 f$ is the directional derivative in the direction $\mathbf{u}$ of the function $D_{\mathbf{u}}f$. Find $D_{\mathbf{u}}^2 f(1,1)$.