C^1 or C^2? Investigating Vector Identity

[madachi]

One of the basic vector identities is

\nabla \cdot (\nabla f \times \nabla g) = 0

Is this true if f and g are C^{1} ? (Or they must be C^{2} functions?

Thanks!

 

[phyzguy]

I think this follows from the equality of mixed partial derivatives. So I think that f and g must be al least twice differentiable for this to hold.