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What property of lagrangian is used here?

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Hi, the attached picture shows a derivation of what I can only assume to be the property that the lagrange equations are invariant under a transformation of the coordinates.
But I have some trouble understanding how you go from the term pointed out the rear of the arrow to the point pointed out by the front of the arrow. Can anyone explain?
 

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dextercioby
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It's really easy

[tex] \frac{\partial q^{i}}{\partial \dot{Q}^{j}} = 0 [/tex]

then he used the equality written on the first line just before the text written (apparently) in some Nordic language.
 

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