The Chain Rule & Implicit Differentiation · Medium problem

A differentiable function $u(x,y)$ is written in polar coordinates $x = r\cos\theta$, $y = r\sin\theta$. At the point with $r = 2$, $\theta = \dfrac{\pi}{6}$ you know $\dfrac{\partial u}{\partial r} = 3$ and $\dfrac{\partial u}{\partial \theta} = 8$. Find the length of the gradient, $|\nabla u| = \sqrt{u_x^2 + u_y^2}$, at that point.