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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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    Are you assuming $b$ is also differentiable?2012-01-25
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    no, just bounded unfortunately. Is there anything I can assume since b(t) is bounded => f(t) is bounded => f' can only be unbounded for limited periods2012-01-25
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    See the example I gave in a comment to marty's answer. Nothing about boundedness implies differentiability. Therein lies your problem.2012-01-25
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    thanks everyone email from the prof says i can chose b, so this is trivial2012-01-25

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