When to Use f = -dU/dx with External Energy Sources?

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In the above video , at time 3:45 to 3:49 he used the formula ##\frac{-dU}{dx}##
There is a comment which says
How can u use f=- du/dx. In case when there is external source of energy?

And answer given to this comment is as follows

In this case we can do this. As here you can calculate and see that the gain in kinetic energy of slab is exactly same that of the change in field energy of capacitor and sum of the two is the work done by battery so it
will not make any difference.


I don't understand the question as well as answer . Why we can't use ##\frac{-dU}{dX}## when external source of energy is present?
 
on Phys.org
gracy said:
I don't understand the question
You should ask the person who asked the question. We would just be guessing

It is hard enough to answer your own questions to your satisfaction that I do not think that it will be productive for us to try and answer someone else's question to your satisfaction.

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