Stoke's and Gauss's Theorum in proving div(curlA)=0

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SquidgyGuff
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Homework Statement


The problem puts forth and identity for me to prove:
Equation: divergence of (curl of vector A) equals zero, written as nabla dot (nabla cross A) = 0.
or
Equation div(curl A) = 0 written in plain mathematical notation.
. It says that I can use "straight-forward" calculation to solve this using the definition of nabla or I can use Gauss's and Stoke's Theorum on an example in which I have a solid 3D shape nearly cut in two by a curve C.

Homework Equations


Gauss's divergence theorem written as the integral over closed surface S of vector A dot da equals the integral over volume V of div A dot dv.
Divergence Theorum
Stokes' theorem written as the line integral over closed curve C of A dot dr equals the surface integral over S of curl A dot da.
Stoke's Theorum

The Attempt at a Solution


I just can't seem to figure out how to start this. The two equations above are clearly suited to proving this identity, but I just can't see how.
 
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Discussion

I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
 
ehild said:
I think it is easier to use the definition of Nabla, and the definitions of cross product and dot product.
Oh and I misstated the equality above, it specifies that the div(curlA)=0 then it has continuous second-order derivatives.