The examples given here for example, show that once you know the form of a taylor polynomial as a function of $x$, you can replace the $x$ with another function. It works when you work out the problems but I don't understand why. It would seem that the chain rule would make the taylor polynomial something else.
closed as not a real question by Jonas Meyer, t.b., Jonas Teuwen, Srivatsan, J. M. Dec 13 '11 at 10:35
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