Zeige für Polynomfunktionen

${\displaystyle f\colon {\mathbb {K} }^{n}\longrightarrow {\mathbb {K} }}$

direkt, dass

${\displaystyle {}{\frac {\partial }{\partial x_{i}}}{\frac {\partial f}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}{\frac {\partial f}{\partial x_{i}}}\,}$