Functionn of two random variables.

Could anyone help me with this question please?

Given X and Y are continuous random variables with the following joint probability density function:

i) Obtain the joint probability density function of X and Y − X.

ii) Show that X and Y − X are independent random variables and write down their (marginal)

probability density functions. Identify these distributions

For part (i)

I let U = X and Y = V - X,

My Jacobian value was 1,

and then I got Is this the correct joint p.d.f for X and Y-X?

Also for the marginal of X, I got but I'm not quite sure.