Is there a way to prove the quotient rule using differentials

[pcvrx560]

Specifically, how do you prove the quotient rule using a similar method that Leibniz used for the product rule?: http://en.wikipedia.org/wiki/Product_rule#Discovery_by_Leibniz

I've tried it once for d(u/v) but I keep getting a vdv term in the denominator.

 

[rock.freak667]

y= u/v

when you have

$$\Delta y = \frac{v \Deltau - u \Deltav}{v^2 +v \Delta v}$$

$$\frac{\Delta y}{\Delta x} = \frac{v \frac{\Delta u}{\Delta x} - u \frac{\Delta v}{\Delta x}}{v^2 +v \Delta v}$$

as Δx→ 0, Δv→ 0

 

[pcvrx560]

d'oh, didn't think about vdv as dv approaches zero

thanks!