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Now taking time derivative of (1) and dividing throughout by (1) it is coming ##\dot J=J(\nabla•v)##(##x## and ##X## are coordinates) which is consistent.

But another thing is approximated while doing this ##\frac{d}{dt}(dx_i)=d(\frac{dx_i}{dt})=dv_i## actually I try to prove it by hand but can't....

Will anyone provide me any hints....