Answer
$-(x\textbf{i}+y\textbf{j}+z\textbf{k})(x^{2}+y^{2}+z^{2})^{-3/2}$
Work Step by Step
Gradient field= $\nabla f=\frac{\partial f}{\partial x}\textbf{i}+\frac{\partial f}{\partial y}\textbf{j}+\frac{\partial f}{\partial z}\textbf{k}$
$=\frac{\partial (x^{2}+y^{2}+z^{2})^{-1/2}}{\partial x}\textbf{i}+\frac{\partial (x^{2}+y^{2}+z^{2})^{-1/2}}{\partial y}\textbf{j}+\frac{\partial (x^{2}+y^{2}+z^{2})^{-1/2}}{\partial z}\textbf{k}$
$=-x(x^{2}+y^{2}+z^{2})^{-3/2}\textbf{i}-y(x^{2}+y^{2}+z^{2})^{-3/2}\textbf{j}-z(x^{2}+y^{2}+z^{2})^{-3/2}\textbf{k}$
$=-(x\textbf{i}+y\textbf{j}+z\textbf{k})(x^{2}+y^{2}+z^{2})^{-3/2}$
