In O Level, students are taught that
So naturally, students may think that (a is a constant)
Well, actually that is good pattern spotting, but unfortunately it is incorrect. Do not be too disheartened if you make this mistake, it is a common mistake.
The above is a conceptual error as only holds when n is a constant.
Fortunately, this question is rarely tested, though it is quite possible that it can come up in A Levels.
To fully understand the following steps, it would help read my other post (Why is e^(ln x)=x?) first.
First, we write .
After fully understanding the above steps, you may memorize the formula if you wish:
Memory Tip: If you let a=e, you should get
The above steps involve the chain rule, which I will cover in a subsequent post.