Given a Riemanian manifold X and a positive scalar velocity field v(X) and the length structure $\displaystyle L=integral(1/v(r(t))*sqrt(<r'(t),r'(t)>)dt,0,1)$ where r(t) is some arbitrary path

then derive the isotropic Eikonal equation for the manifold X and prove that it is equal to

$\displaystyle |grad(d(x))| =1/v(x)$

where d(x) is the distance from a source point x0 to x both in X.

and is the length of the minimal geodesic from x0 to x as defined by the riemanian metric and the length structure above.

My problem is that I dont know how to approach this. What constitutes a proof for this?