How would I go about constructing this following proof?

Let f = f (x, y, z) be a function. Show that for any other function v = v(x, y, z)

$\displaystyle \nabla \cdot (\nabla f \times \nabla v) = 0$

I understand you have to show that it is divergence free, but would you just write each vector term in terms of a derivative? :S