how do you use the change of variable:

[itex]\xi[/itex] = x - ct

on the PDE

u

_{t} + c u

_{x} = 0

where u(t,x) = v(t,x-ct) = v(t,[itex]\xi[/itex])

to get

v

_{t} = 0

I am trying to follow the steps of Peter J. Olver in this document

http://www.math.umn.edu/~olver/pd_/lnw.pdf starting on pg 4 but get stuck here...i think i am missing an important calculus concept but cannot figure out what. He says to use the chain rule but i cannot figure out how that helps.

Any help GREATLY appreciated