The Chain Rule & Implicit Differentiation · Easy problem

Let $f(x,y) = x^2 + xy$, and let a point move along the parabola $\mathbf r(t) = \langle t,\ t^2\rangle$. Use the vector form of the chain rule, $\dfrac{d}{dt}f(\mathbf r(t)) = \nabla f(\mathbf r(t))\cdot\mathbf r'(t)$, to find the rate of change of $f$ at $t = 2$.