Let $\displaystyle (r, \theta, z)$ be the cylindrical coordinates in $\displaystyle \mathbb{R}^3$. Derive the Laplacian in cylindrical coordinates.

So what I know is that $\displaystyle x=r\cos\theta, y=r\sin\theta, z=z$, so that the last term in the Laplacian doesn't change.

I know where I want to go (I have the expression right in front of me), but I'm not seeing how to derive the other two.