# I Potential energy in 3D

1. Aug 1, 2017

### Gurasees

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

2. Aug 1, 2017

### olgerm

Which formula do you mean?

3. Aug 3, 2017

### Chandra Prayaga

Derivatives of what?

4. Aug 4, 2017

### jbriggs444

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.