Question

Find the gradient vector field of f. f(x, y, z) = 10 x2 + y2 + z2

Answer 1

Assuming $f(x,y,z)=\dfrac{10}{x^2+y^2+z^2}$, and not $10x^2+y^2+z^2$ (which is easier to work with, but not by much).

$\nabla f(x,y,z)=\left\langle\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right\rangle=\left\langle-\dfrac{20x}{(x^2+y^2+z^2)^2},-\dfrac{20y}{(x^2+y^2+z^2)^2},-\dfrac{20z}{(x^2+y^2+z^2)^2}\right\rangle$