方向微分
f ( v ) = f 1 ( f 2 ( v ) ) {\displaystyle {\boldsymbol {f}}({\boldsymbol {v}})={\boldsymbol {f}}_{1}({\boldsymbol {f}}_{2}({\boldsymbol {v}}))} なら、 ∂ f ∂ v ⋅ u = ∂ f 1 ∂ f 2 ⋅ ( ∂ f 2 ∂ v ⋅ u ) {\displaystyle {\frac {\partial {\boldsymbol {f}}}{\partial {\boldsymbol {v}}}}\cdot {\boldsymbol {u}}={\frac {\partial {\boldsymbol {f}}_{1}}{\partial {\boldsymbol {f}}_{2}}}\cdot \left({\frac {\partial {\boldsymbol {f}}_{2}}{\partial {\boldsymbol {v}}}}\cdot {\boldsymbol {u}}\right)} 。