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When I do the following transformation:

$$

X_1=x_1+x_2 \\

X_2=x_2

$$

It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have:

$$

dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2

$$

So we have ##dx_1dx_1=0##. Is this kind of weird? Why does ##(dx_1)^2## have to be 0?

Thank you!

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# A question about Jacobian when doing coordinates transformation

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