How can I get the expression of the pdf of Y for y = f(x1, ... , xN) , knowing every distribution associated to X1, ... , XN?

Question

Basically, the title says it all. I dispose of a function f that serves as logic to data fusion from the measures x1, ... , xN : I would like to, not using Monte Carlo or similar methods, analitically find out the pdf of Y, the random variable associated to y. I am writing a matlab .mlx file so I dispose of the symbolic expressions of f(x1, ... , xN) and of the PDFs of the Xi associated to each xi.

Is it possible in any way, and how ?

Thank you.