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

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The discussion centers on understanding a specific differential expression and its implications. The user is seeking clarification on the differential of a given expression, particularly focusing on the equation where the partial derivative of H_i^j with respect to x equals zero. There is a request for the physical meaning or background of the related 4x4 quantity to aid in further investigation. The conversation highlights the need for deeper insights into the mathematical framework and its applications. Understanding these differentials is crucial for advancing knowledge in the relevant field.
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 ?
 
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