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take v(velocity) to be a function of x and x to be a function of t(time).

then dv/dt=vdv/dx thats cool

but in the hint in problem 2.12 classical mechanics by john r taylor he equates vdv/dx and 1/2(dv^2)/dx

that is- vdv/dx=1/2(dv^2)/dx

Could someone please explain this?