Ill help you get the answer but i cant give it for every single one so ill give you some rules to use...
If you differentiate

then you get

. (n being a real number)
Re-write problem 1 as

and use the above on that...
The chain rule will come in useful for a lot of these...
Chain rule - Wikipedia, the free encyclopedia
Use the Quotient Rule for question 4... Give it a try and see how you get on.
Product rule:

.
Ill use your question 5 as an example...
In this case we have

and

. So we leave 'u' as it is and differentiate sin3x (using the chain rule) to get 3cos3x. Then leave 'v' as it is and differentiate cos2x to get -2sin2x. Now add these together to get

.