ナブラ
∇ ( f g ) = f ∇ g + g ∇ f {\displaystyle \nabla (fg)=f\nabla g+g\nabla f}
∇ ( u ⋅ v ) = u × ( ∇ × v ) + v × ( ∇ × u ) + ( u ⋅ ∇ ) v + ( v ⋅ ∇ ) u {\displaystyle \nabla ({\boldsymbol {u}}\cdot {\boldsymbol {v}})={\boldsymbol {u}}\times (\nabla \times {\boldsymbol {v}})+{\boldsymbol {v}}\times (\nabla \times {\boldsymbol {u}})+({\boldsymbol {u}}\cdot \nabla ){\boldsymbol {v}}+({\boldsymbol {v}}\cdot \nabla ){\boldsymbol {u}}}
∇ ⋅ ( f v ) = f ( ∇ ⋅ v ) + v ⋅ ( ∇ f ) {\displaystyle \nabla \cdot (f{\boldsymbol {v}})=f(\nabla \cdot {\boldsymbol {v}})+{\boldsymbol {v}}\cdot (\nabla f)}