This is where you are required to derive a function within a function (otherwise known as composite functions, recall pre calc 12). In chain rule there are cases where you will have to use power, product, quotient rules etc. for the inner function–or even chain again! You should have a good basis in all the previous rules, so feel free to go back and review 2.2-2.5 if needed.
Chain Rule For Finding Derivatives (cr: Organic Chem Tutor)
Applying the chain rule twice (cr: Khan Academy)
Derivatives of Radical Functions (cr: Organic Chem Tutor)
Trig Derivatives using the Chain Rule (cr: Physics and Math Tutor)