- #1

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## Homework Statement

I have noticed that in some calculations they use $$ \vec{\nabla}\cdot\vec{u}=\frac{1}{V}\frac{dV}{d\tau}$$. I would like to derive it.

## Homework Equations

##\vec{u}=(\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})##

##\vec{A}\cdot\vec{B}=A^{\mu}B_{\mu}##

##\vec{\nabla}=(\frac{d}{dt},\frac{d}{dx},\frac{d}{dy},\frac{d}{dz})##

## The Attempt at a Solution

$$ \vec{\nabla}\cdot\vec{u}=\frac{d}{dt}\frac{dt}{d\tau}+\frac{d}{dx}\frac{dx}{d\tau}+\frac{d}{dy}\frac{dy}{d\tau}+\frac{d}{dz}\frac{dz}{d\tau}=... $$May I do this?

$$...=\frac{d}{d\tau}(\frac{dt}{dt}+....)??$$

I guess not, because ##\frac{d}{d\tau}(\frac{dt}{dt})=\frac{d}{d\tau}1=0##. Please advise.