Homogeneous polynomial/Representation with formal partial derivatives/Exercise

Let ${}H\in K[X_{1},\ldots ,X_{n}]$ be a homogeneous polynomial of degree ${}e$. Show the equality

${}eH=X_{1}{\frac {\partial H}{\partial X_{1}}}+\cdots +X_{n}{\frac {\partial H}{\partial X_{n}}}\,.$

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