People here at MHF are not fond of those who post a whole bunch of questions piled up into one post. I will start off by helping you with the chain rule for the first of these questions. With that, you should be able to do the 2nd, 3rd and 4th problems.

Apply the chain rule when deriving this function.

Those question marks are to be filled with what you are supposed to tack on for the chain rule. When a function has functions nested in it like so: , then the derivative follows through like a chain:

Therefore....

Remember one last thing here; you are deriving with respect to x. Other variables are then treated as constants, hence why the "r" and "t" followed through as coefficients.