I've just done a derivation and had to use the following(adsbygoogle = window.adsbygoogle || []).push({});

[itex]u_{b}u^{c}\partial_{c}\rho = u_{b}\frac{dx^{c}}{d\tau}\frac{\partial\rho}{\partial x^{c}} = u_{b}\frac{d\rho}{d\tau}[/itex]

We've done this cancellation a lot during my GR course, but I'm not clear exactly when/why this is possible.

EDIT: is this only true in inertial coordinates?

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# When do total differentials cancel with partial derivatives

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