How to derive curl in spherical coordinates This is one of those questions where I know I am making a dumb mistake someplace and I am trying to check where it is. 
$$
        \begin{vmatrix}
        \frac{\bf\hat r}{r^2\sin\theta} & \frac{\bf\hat \theta}{r\sin\theta} & \frac{\bf \hat\phi}{r} \\
        \frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial \phi} \\
        u_r & ru_{\theta} & r\sin\theta u_{\phi} \\
        \end{vmatrix}=\nabla \times \bf u
$$
So far so good, but for some reason when I take the determinant I am not gettinghte usual formula for $\nabla \times \bf u$. So let's break it down: 
Term 1: $\frac{\bf\hat r}{r^2\sin\theta} \left[\frac{\partial}{\partial \theta}(r\sin\theta u_{\phi})-\frac{\partial}{\partial \phi}( ru_{\theta} )\right]=\frac{\bf\hat r}{r\sin\theta} \left[\frac{\partial}{\partial \theta}(\sin\theta u_{\phi})-\frac{\partial u_{\theta}}{\partial \phi}\right]$
so far so good. 
But then I get to term 2. it should be:  $\hat\theta\frac{1}{r}\left[\frac{1}{\sin \theta}\frac{\partial u_r}{\partial \phi}- \frac{\partial}{\partial r}(ru_{\phi})\right]$
but I get:  $\hat\theta\frac{-1}{r\sin\theta}\left[\frac{\partial}{\partial r}(r\sin\theta u_{\phi})- \frac{\partial}{\partial \phi} (u_r)\right]=\hat\theta\frac{1}{r}\left[-\frac{\sin\theta u_{\phi}}{\sin \theta}+\frac{\partial u_r}{\partial \phi}\frac{1}{\sin \theta} \right]=\hat\theta\frac{1}{r}\left[-{u_{\phi}}+\frac{\partial u_r}{\partial \phi}\frac{1}{\sin \theta} \right]$
(The -1 in the second term is b/c when taking a determinant you subtract the second term) 
anyhow i get the sense i did something silly. But  am having trouble figuring out what. 
thanks folks. 

If
$\frac{\partial}{\partial r}(ru_{\phi}) = u_{\phi}$
then you're all right.  Everything else looks the same in that component of the curl.
As long as $u_\phi$ doesn't depend on $r$, it should, right?
