And we're taking the limit as x gets closer and closer and closer to a. So this is just another way of writing the definition of the derivative. So that's fine. Let's do the same thing for g prime of a. So f prime of a over g prime of a is going to be this business, which is in orange, f prime of a over g prime of a, which we can write as the limit as x approaches a of g of x minus g of a over x minus a. Well, in the numerator we're taking the limit as x approaches a. In the denominator we're taking the limit as x approaches a.