What is the relationship between total variation Δf, δf, and Δx?

[matematikuvol]

Total variation is defined by

$$\Delta f=\delta f+\Delta x$$

For example $$f(x,y)=yx$$, $$y=y(x)$$

$$\Delta f=x\delta y+\Delta x$$

How is defined $$\Delta x$$. Is that rate of change of x, while y is constant?

 

[chiro]

Hey matematikuvol.

The best way to think about Δx is basically a delta. If Δx = dx then we would be referencing an infinitesimal, but otherwise it is going to be some small non-infinitesimal number.

This might help you out:

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

 

[matematikuvol]

What's difference between total derivative, and total variation?