The equation of f'(x) has been given in the previous step, and f'(a) is to substitute a into the equation. F'(a)=0 because the result of x-a is 0.
Moreover, because g(a) and g'(a) are not zero, g(x) is a continuous function, and f'(a) has a limit value, so it is necessary to limit F "(a) to get accurate results.