∂ ( f 1 , … , f m ) ∂ ( x 1 , … , x n ) \frac{\partial\left(f_{1}, \ldots, f_{m}\right)}{\partial\left(x_{1}, \ldots, x_{n}\right)} ∂(x1,…,xn)∂(f1,…,fm) J = [ ∂ f ∂ x 1 ⋯ ∂ f ∂ x n ] = [ ∂ f 1 ∂ x 1 ⋯ ∂ f 1 ∂ x n ⋮ ⋱ ⋮ ∂ f m ∂ x 1 ⋯ ∂ f m ∂ x n ] \mathbf{J}=\left[\begin{array}{ccc} \frac{\partial \mathbf{f}}{\partial x_{1}} & \cdots & \frac{\partial \mathbf{f}}{\partial x_{n}} \end{array}\right]=\left[\begin{array}{ccc} \frac{\partial f_{1}}{\partial x_{1}} & \cdots & \frac{\partial f_{1}}{\partial x_{n}} \\ \vdots & \ddots & \vdots \\ \frac{\partial f_{m}}{\partial x_{1}} & \cdots & \frac{\partial f_{m}}{\partial x_{n}} \end{array}\right] J=[∂x1∂f⋯∂xn∂f]=⎣⎢⎡∂x1∂f1⋮∂x1∂fm⋯⋱⋯∂xn∂f1⋮∂xn∂fm⎦⎥⎤ J i j = ∂ f i ∂ x j \mathbf{J}_{i j}=\frac{\partial f_{i}}{\partial x_{j}} Jij=∂xj∂fi
