I am studying multivariate statistics and I don't understand the meaning of Jacobian of the transformation for pdf of function of random vectors.
If I have a random vector, let's say bivariate, (X,Y) with joint density f(X,Y) I know how to find the joint pdf of (U,V) with U = g(X,Y) and V = h(X,Y) I did a lot of exercises and I can easily calculate joint pfd of functions of random vectors.
The formula for joint pdf of functions of random vectors involves the determinant of the Jacobian matrix of inverse functions. In the univariate case I understand that I have a derivative because the pdf is the derivative of the CDF. In the multivariate case why the determinant of the Jacobian?