ナブラ
とは異なる。
また∇の微分的な性質を用いた反例としては、
( ∇ x ) × ( ∇ y ) = ( x ^ ∂ x ∂ x + y ^ ∂ x ∂ y + z ^ ∂ x ∂ z ) × ( x ^ ∂ y ∂ x + y ^ ∂ y ∂ y + z ^ ∂ y ∂ z ) = x ^ × y ^ = z ^ {\displaystyle (\nabla x)\times (\nabla y)=\left({\hat {\boldsymbol {x}}}{\frac {\partial x}{\partial x}}+{\hat {\boldsymbol {y}}}{\frac {\partial x}{\partial y}}+{\hat {\boldsymbol {z}}}{\frac {\partial x}{\partial z}}\right)\times \left({\hat {\boldsymbol {x}}}{\frac {\partial y}{\partial x}}+{\hat {\boldsymbol {y}}}{\frac {\partial y}{\partial y}}+{\hat {\boldsymbol {z}}}{\frac {\partial y}{\partial z}}\right)={\hat {\boldsymbol {x}}}\times {\hat {\boldsymbol {y}}}={\hat {\boldsymbol {z}}}}