To perform the differentiation, you must realise that you are not differentiating x^n, but instead (something else)^n, so the chain is this ‘something else’. We continue to differentiate the expression as though we are differentiating x^n, but we must multiply the result by the derivative of the ‘something else’. This is the chain rule. But once we perform the chain, we do not differentiate any further term.

Later in this topic you will notice special cases (like sin^3 2x) where chain rule is performed more than once.