Hey yob007.

The f'(g(x)) just means f'(g(cos(4x5+lnx))).

For the other two, just differentiate the expressions and show when the derivative doesn't exist (either from the domain or when the derivative can't be computed).

For the last set of questions, show us what you have tried and what you have thought about: doesn't matter if its a partial answer or an incomplete brainstorm.