The Value of An N-Order Jacobian Determinant

Making use of the properties of eigenvalue and rank of matrices,the value of the determinant of the following Jacobian matrix is given:
J=((∂y_i)/(∂x_j))_n×n, y_i=(x_i)/(???19860314???x_k²); i,j=1,2,...,n; extending the result in1to the case of n-dimensions This method is much simpler than that based on the fundamental properties of determinants.