- #1

- 69

- 0

## Homework Statement

What exactly is a total derivative? What is the definition of this concept?

## Homework Equations

An example of total derivatives:

## The Attempt at a Solution

I've tried searching for it, but found no helpful information.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Cinitiator
- Start date

- #1

- 69

- 0

What exactly is a total derivative? What is the definition of this concept?

An example of total derivatives:

I've tried searching for it, but found no helpful information.

- #2

SammyS

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

- 11,377

- 1,038

What you have is a differential, not a derivative.## Homework Statement

What exactly is a total derivative? What is the definition of this concept?

## Homework Equations

An example of total derivatives:

## The Attempt at a Solution

I've tried searching for it, but found no helpful information.

- #3

- 1,335

- 40

- #4

- 428

- 1

## Homework Statement

What exactly is a total derivative? What is the definition of this concept?

## Homework Equations

An example of total derivatives:

## The Attempt at a Solution

I've tried searching for it, but found no helpful information.

You may contrast your "total derivative", with partial derivative. The total is sort of an absolute change, like if you have a (k,l)(t) path, and head in the (dk,dl) direction. You can contrast this with the partial derivatives, f

- #5

- 546

- 10

- #6

- 428

- 1

You may contrast your "total derivative", with partial derivative. The total is sort of an absolute change, like if you have a (k,l)(t) path, and head in the (dk,dl) direction. You can contrast this with the partial derivatives, f_{k}and f_{l}, which would contribute to parts of the total derivative. Or, you might have a path k(l), so you could find the total derivative along that path. Another definition of total derivative, would be the vector (f_{k},f_{l}), otherwise known as the gradient. The tricky part is, the various realizations of the term total derivative can be a little confusing, I don't think I happened to notice all this until I graduated and had a chance to look back at all the contexts I had seen it.

I was hoping to pull together the various definitions of total derivative from

http://en.wikipedia.org/wiki/Total_derivative

It includes Jacobian, gradient (special case of Jacobian), and, somehow consistent with that, a gradient dotted with a path vector, which could be parametrized by one of the original independent variables. I suppose the latter is like the former in that it is the total change as we move along in t, or in a way, in x, so we contrast df/dx with ∂f/∂x, another strangeness.

Share: