Second Derivatives of Vectors
1. ∇ × (∇f) = 0
$$\frac{\partial}{\partial x} \frac{\partial f}{\partial y} - \frac{\partial}{\partial y} \frac{\partial f}{\partial x}$$
Let f(x, y, z) be a scalar field. First express ∇f in a Cartesian basis.
(i.e. in terms of i, j, k)
Now take ∇ × (∇f) and show that it is zero no matter what f is.
