Assuming [tex]f(x,y,z)=\dfrac{10}{x^2+y^2+z^2}[/tex], and not [tex]10x^2+y^2+z^2[/tex] (which is easier to work with, but not by much).
[tex]\nabla f(x,y,z)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right\rangle=\left\langle-\dfrac{20x}{(x^2+y^2+z^2)^2},-\dfrac{20y}{(x^2+y^2+z^2)^2},-\dfrac{20z}{(x^2+y^2+z^2)^2}\right\rangle[/tex]
