# Why Jacobian matrix is a special case of alternant matrix?

I don't quite understand why a standard Jacobian matrix $$JF(x) = \left[{\partial F_i\over \partial x_j}\right]_{ij}$$

Because I think Jacobian matrix uses the same $$\alpha$$, or the same variate in the expression, so it is not a alternant matrix.

Define $$f_i(x)={\partial F_i(x)\over \partial x}$$and try to represent $$J\ F(x)$$ as a matrix with entries being of form $$f_i(x_j)$$.