Ordinary and symbolic powers are Golod

Let $S$ be a positively graded polynomial ring over a field of characteristic 0, and $I\subset S$ a proper graded ideal. In this note it is shown that $S\mathrm{/}I$ is Golod if $\mathrm{\partial }(I{)}^2\subset I$. Here $\mathrm{\partial }(I)$ denotes the ideal generated by all the partial derivatives of elements of $I$. We apply this result to find large classes of Golod ideals, including powers, symbolic powers, and saturations of ideals.