Wronskian is an inbuilt function:
y = {x^3 + 2 x^2, 3 x^2 - 2 x, 14 x^2 - x^5, 9 x^2 + 2 x + 6, 2 x^2 + 5 x + 6};
Wronskian[y, x]
(* -43200 x *)
The matrix:
m = Table[D[y[[i]], {x, j}], {i, Length[y]}, {j, 0, Length[y] - 1}];
m // MatrixForm
Det[m]
(* -43200 x *)