∇ v f ( x ) , {\displaystyle \nabla _{\mathbf {v} }{f}(\mathbf {x} ),} f v ′ ( x ) , {\displaystyle f'_{\mathbf {v} }(\mathbf {x} ),} D v f ( x ) , {\displaystyle D_{\mathbf {v} }f(\mathbf {x} ),} D f ( x ) ( v ) , {\displaystyle Df(\mathbf {x} )(\mathbf {v} ),} ∂ v f ( x ) , {\displaystyle \partial _{\mathbf {v} }f(\mathbf {x} ),} v ⋅ ∇ f ( x ) , {\displaystyle \mathbf {v} \cdot {\nabla f(\mathbf {x} )},} v ⋅ ∂ f ( x ) ∂ x . {\displaystyle \mathbf {v} \cdot {\frac {\partial f(\mathbf {x} )}{\partial \mathbf {x} }}.}