Well, as far as I have been taught and know :$$\vec F = -dU/dx $$ But then my teacher also told me that when the derivative of potential energy is zero the $"net"$ Forces are zero.
But this contradicts both my book and my professor, as he had also said that the above statement comes from the fact that :
The work done by any force is integral of the dot product Force $\vec F$ and an infinitely small displacement $d\vec r$; where $\vec F$ represents a particular force and not the net force.
And I know that :
Work done by a conservative force is equal to negative of the change in potential energy.
So am I missing something here?
I viewed the similar questions but those didn't answer my query.