Answer
$\nabla f (x, y, z)=\dfrac{1}{(x^2+y^2+z^2)} (xi+yj+zk)$
Work Step by Step
Re-write as: $f(x,y,z)=\dfrac{1}{2} \ln (x^2+y^2+z^2)$
Thus, the gradient field can be computed as
$\nabla f (x, y, z)=\dfrac{1}{2} [\dfrac{2x}{(x^2+y^2+z^2)}i +\dfrac{2y}{(x^2+y^2+z^2)} j +\dfrac{2z}{(x^2+y^2+z^2)} k ]$
or, $\nabla f (x, y, z)=\dfrac{1}{(x^2+y^2+z^2)} (xi+yj+zk)$
