Potential Energy in 3D: Partial Derivatives

[Gurasees]

To find potential energy in 3 dimensions why do we take partial derivative and not total derivative?

 

[olgerm]

Which formula do you mean?

 

[Chandra Prayaga]

Derivatives of what?

 

[jbriggs444]

To find potential energy in 3 dimensions why do we take partial derivative and not total derivative?

Guessing at the context...

If you have the potential field (e.g. gravitational potential per unit mass as a function of position), you can take three partial derivatives to arrive at the associated vector field (e.g. gravitational acceleration as a function of position).

If you have the vector field (e.g. gravitational acceleration as a function of position) and an assurance that the field is conservative then you can arbitrarily assign a zero potential somewhere, and take a path integral along an arbitrarily chosen path to obtain the associated potential field (e.g. gravitational potential per unit mass as a function of position).

What would it mean to take the total derivative of a function of three variables? The only way I see to do it would be to choose a path (or at least a tangent to a path). Taking a partial derivative amounts to picking a tangent that is aligned with a chosen coordinate axis.