Basic Irrotational Flow Question

It's easy to do it if you go into suffix notation.

$[\nabla \times \nabla \phi]_i = \epsilon_{ijk} \frac{\partial}{\partial x_i} \frac{\partial \phi}{\partial x_j}$.

It is easy to show that this equals zero due to the fact that $\frac{\partial^2 \phi}{\partial x_i \partial x_j}= \frac{\partial^2 \phi}{\partial x_j \partial x_i}$ and $\epsilon_{ijk}$ is anti symmetric.

If you need any more help, just quote and post back and ill do my best to help

Ok, so I guess then that we're trying to show $\nabla \times u = \nabla \times \nabla \phi = 0$.

What is the epsilon notation that you are using? Cheers for the help btw, I'll rep afterwards

$\varepsilon_{ijk}$ is the Levi-Civita symbol and is incredibly useful with this kind of thing. Are you familiar with suffix notation? Because I don't think you can represent the cross product of two vectors in suffix notation without it (not easily at least).