How I can get the equation (2.25)? What is the calculation? If $|x|$ is the length of the vector, I can't see how to do partial differential with respect to a length?
Can someone help me? It is really important for me. I have been thinking it since last night. Thanks for any help! Thanks!
I think the first equation of that line is a bit confusing. Instead notice that the normal is $x/|x|$, which is the gradient of $f(x)=|x|$, which is in turn because the sphere is the level set of $f$. Therefore
$$\frac{\partial G}{\partial \nu} = \lim_{t \to 0} \frac{G(x+tx/|x|) - G(x)}{t}$$
You can in turn calculate this as $\nabla G \cdot (x/|x|)$.