The Chain Rule & Implicit Differentiation · Challenge problem

Let $u(x,y) = e^x\cos y + x^2y^2$, and write $u$ in polar coordinates $x = r\cos\theta$, $y = r\sin\theta$. Evaluate $u_{rr} + \dfrac{1}{r}u_r + \dfrac{1}{r^2}u_{\theta\theta}$ at $r = 1$, $\theta = \dfrac{\pi}{4}$.