Hessian of a function Given this equation: $f(x,y,z) = \sqrt{1+x^2+y^2+z^2}$
I tried to calculate the Hessian --> for example $\frac{\partial f}{\partial x} = \frac{x}{\sqrt{1+x^2+y^2+z^2}}$ The second derivativ respect to x is hard to calculate for me: I tried the product rule: $x*(1+x^2+y^2+z^2)^{-1/2}$.
Then i get: $\frac{1}{1+x^2+y^2+z^2} - \frac{x^2}{(1+x^2+y^2+z^2)^{3/2}}$
But this is wrong.
Could anyone help?

What you get it's quite correct, because $$\frac{\partial f}{\partial x^2}=\frac{1}{\sqrt{1+x^2+y^2+z^2}}-\frac{x^2}{(1+x^2+y^2+z^2)^{3/2}}$$ 
And making some algebra you get $$\frac{\partial f}{\partial x^2}= \frac{1+y^2+z^2}{(1+x^2+y^2+z^2)^{3/2}}$$
I think that the other may be similar to this
