Graduate What will be value of this differential? Kindly help and explain

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SUMMARY

The discussion centers on understanding the differential of a specific expression involving the partial derivative \(\frac{\partial H_i^j}{\partial x}=0\). Participants seek clarification on the physical meaning of this equation and its implications in a broader context. The inquiry emphasizes the need for a deeper investigation into the first 4x4 quantity related to this differential, indicating its significance in the relevant field of study.

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ssafdarpk
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Can someone help me understand the answer to this differential?

I have the following expression
1651869542261.png
where
1651869584718.png

Now what I can understand the differential of
1651869641031.png

what will be the following?
1651869676443.png
 
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ssafdarpk said:
where
1651869584718-png.png

Now what I can understand the differential of
1651869641031-png.png
From these equations it seems \frac{\partial H_i^j}{\partial x}=0 holds. Could you tell me physical meaning or background of the first 4x4 quantity for further investigation ?
 
Last edited:
I've encountered a few different definitions of "indefinite integral," denoted ##\int f(x) \, dx##. any particular antiderivative ##F:\mathbb{R} \to \mathbb{R}, F'(x) = f(x)## the set of all antiderivatives ##\{F:\mathbb{R} \to \mathbb{R}, F'(x) = f(x)\}## a "canonical" antiderivative any expression of the form ##\int_a^x f(x) \, dx##, where ##a## is in the domain of ##f## and ##f## is continuous Sometimes, it becomes a little unclear which definition an author really has in mind, though...

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