Where are you stuck, particularly?

Stuff:

(a) They are independent so you can multiply the two uniform densities to find the joint density... I assume you know the density for U(0,1).

(b) ...Do the integration. Figure out your bounds by inspecting [0,1]/[0,1]. You may have some questions about bounds.

(c) You have the formula in your notes... Post any questions about transforming/computing Jacobian...etc.