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I was wondering for the bounded function $b(t)$ what statements can be made about the derivative of

$f(t)=exp(b(t))$

specifically it would be nice if the derivative f' were bounded.

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    thanks everyone email from the prof says i can chose b, so this is trivial2012-01-25

1 Answers 1

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Only if b'(t) is bounded, since f'(t) = b'(t) exp(b(t)).

Try $b(t) = sin(t^2)$.

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    I was thinking: Try $b(t) = \log(1 + \chi_{\mathbb{Q}}(t))$.2012-01-25