>> So presumably the derivative of f(f(f(x))) is going to be something 
>> like f'(f(f(x))) * f'(f(x)) * f'(x)? And in general, the Nth 
>> composition will be ever more complex as N increases?
>>
>> Oh dear.
> 
> Ooo, but wait... The Nth derivative of a polynomial will be zero if N 
> exceeds the order of the polynomial. Hmm.

...which doesn't help, because the derivative of the Nth iterate will be

   f'(x) * f'(f(x)) * f'(f(f(x)) * f'(f(f(f(x))) * ...

which involves only the first derivating of f and the iterates of f.

Damnit, I really suck at math. :'{

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