Not homework, but I was just curious whether or not there exists a function which satisfies:
$\ f'(x)=f(f(x))$
I tried differentiating both sides and working from there, but just arrived at nonsense.
Thanks.
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Try $f(x)=0$, for all $x$. – vadim123 Jun 04 '13 at 20:04
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1@vadim123 Obviously the OP looks for a non trivial solution. – Jun 04 '13 at 20:12