The problem and its solution is given here :
A difficulty in understanding the solution of a problem.
But I do not understand how $f_{x_{k}x_{k}}^{''} = -k(k + 1) c^{\frac{n^2 + n -2}{2}}$ and $f_{x_{k}x_{j}}^{''} = -k(j) c^{\frac{n^2 + n -2}{2}}$ , could anyone explains this for me please?