# When the derivative of potential energy is equal to zero why are the net forces zero?

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.

• In your professor's scenario were all forces conservative so that the net force is also conservative? Apr 23, 2020 at 17:30
• Not always, in one scenario that he took to explain this, there was friction acting only along horizontal part of the surface Apr 23, 2020 at 17:39

You are correct. The equation $$\vec{F}=- \vec{\nabla} U$$ is only valid for a conservative force.