Let u(x, y) be a twice differentiable function. Show that in polar coordinates $\displaystyle x = r \cos(\theta), y = r \sin(\theta)$ the Laplacian of u takes the form...

$\displaystyle u_{xx} + u_{yy} = u_{rr} + \frac{1}{r} u_{r} + \frac{1}{r^2} \frac{{\partial}^2 u}{{\partial} {\theta}^2}$.

Should be an easy Q but i cant remember how to do the second derivative.

$\displaystyle u_{x} = u_{r} \frac{\partial r}{\partial x} + u_{\theta} \frac{\partial \theta}{\partial x} $ = $\displaystyle u_{r} \frac{x}{r} + u_{\theta} \frac{-y}{r^2} $.

But then how do you take the second derivative?