I am learning derivatives but don't understand why one is allowed to drop the lim just before putting the solution into the square.

Question

anonymous · Answer

I'm not sure what you mean by "putting the solution into the square"; can you be a bit more specific?

anonymous · Answer

Sorry, when I asked this I thought this open study website had something to do with the MIT Open Courseware.  In the attached file you can see the solution is under the wavy line and it is in a square (literally a drawn square).
If you look at my notes (which reflects the lecturer's solution) you will see that before the answer in the drawn square is a lim (as delta x approaches 0).
The professor does away with it and I don't know why he is allowed to do it.
Thank you for your help.  (attachment is notes from a lecture in which the professor solves derivative inside the question marks.

anonymous · Answer

The last step with a limit is $\displaystyle\lim_{\Delta x\rightarrow 0}nx^{n-1}$.  You can get rid of the limit because there is no $\Delta x$ in the equation...so it doesn't matter what $\Delta x$ is doing.

anonymous · Answer

That makes sense.  Thank you so much!