is this accurate?

Question

''me returning to my lim x--> c f(x)/g(x) to see that it has now been reduced to x --> c f('x)/g'(x)''

Answer 1

No, that is not accurate. The correct transformation when differentiating a limit is as follows:

If you have the function lim x→c f(x)/g(x), then differentiating it gives lim x→c f'(x)/g'(x). The prime notation (') indicates the derivative of a function.