Finding the differential of an expression with multiple variables

ssafdarpk · May 6, 2022

Can someone help me understand the answer to this differential?

I have the following expression

Product of three matrices: a 4x2 matrix with entries 1 - x/L, 0, x/L, 0 and 0, 1 - x/L, 0, x/L; a 2x4 matrix with entries +L d/dH0(dH0/dx), +L d/dH1(dH1/dx) and -L d/dH0(dH0/dx), +L d/dH1(dH1/dx); and a 4x2 matrix with entries 1 - x/L, 0, x/L, 0 and 0, 1 - x/L, 0, x/L.

where

Now what I can understand the differential of

Equation: partial of H_i with respect to x equals a row vector [-1/L, 1/L] multiplied by the column vector [H_i^1, H_i^2].

what will be the following?

Handwritten expression: partial derivative with respect to H_i of the partial derivative of H_i with respect to x, followed by =??

anuttarasammyak · May 6, 2022

ssafdarpk said:

where

Now what I can understand the differential of

From these equations it seems [tex]\frac{\partial H_i^j}{\partial x}=0[/tex] holds. Could you tell me physical meaning or background of the first 4x4 quantity for further investigation ?

Finding the differential of an expression with multiple variables

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