Solving for ΔP: Should I Include ΔVΔI?

[Kyouran]

Hey all,

I have a question that's been annoying me for a little while:

if i have

$$P_0 = V_0 I_0$$

(power equals current times the potential difference) then is

$$P_0 + \Delta P= V_0 I_0 + V_0 \Delta I + I_0 \Delta V + \Delta V \Delta I$$

correct or should it be

$$P_0 + \Delta P= V_0 I_0 + V_0 \Delta I + I_0 \Delta V$$

In other words, if I use ΔP should I include the term ΔVΔI or not? After all, when I use differentials, i get

$$\frac{dP}{dt} = V_0 \frac{dI}{dt} + I_0 \frac{dV}{dt}$$

But when I look at what is meant by "ΔP", it is stated as "the change in delta P", which includes more terms than just the first order ones? What is exactly meant by Δ? Just the first order variation, or all orders of variations?

Thanks in advance,


Kyouran

 

[HomogenousCow]

The product of the two differences can be taken to zero as we approach the limit to 0, so you do regain the usual differential P+dP=IV+IdV+VdI