# Is my thinking correct for partial derivatives and tensors?

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?

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