∂
多変数ベクトル値関数の勾配ベクトルを縦に並べたものをヤコビ行列(やこびぎょうれつ、英: Jacobian matrix)または関数行列と呼び、∂記号を用いて次のように表す。
∂ f ∂ x = ∂ ( f 1 , f 2 , ⋯ , f m ) ∂ ( x 1 , x 2 , ⋯ , x n ) = ( ∂ f 1 ∂ x 1 ⋯ ∂ f 1 ∂ x n ⋮ ⋱ ⋮ ∂ f m ∂ x 1 ⋯ ∂ f m ∂ x n ) {\displaystyle {\frac {\partial \mathbf {f} }{\partial \mathbf {x} }}={\frac {\partial (f_{1},f_{2},\cdots ,f_{m})}{\partial (x_{1},x_{2},\cdots ,x_{n})}}={\begin{pmatrix}{\cfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\cfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}}