So I was transforming the affine connection and I ended up with a term like this: $$ \frac{\partial^2 x'^a}{\partial x'^b \partial x^p} $$

where $x$ and $x'$ are two different coordinate systems

Luckily there were two of these and they cancelled, however, does this term equal 0?

Part of me thinks so as $\frac{\partial x'^a}{\partial x'^b}=\delta ^a_b$ however for a later question doing this didn't work.

Also, do partial derivatives still commute if we differentiate with respect to different coordinate systems?

  • $\begingroup$ If they cancelled, you'd better hope they don't equal zero. $\endgroup$ – Paul Aug 21 at 15:29
  • $\begingroup$ @Paul I assume he meant a cancellation in the context of a sum of identical terms with opposite sign. $\endgroup$ – aRockStr Aug 21 at 19:38

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