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.
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.
Only if b'(t) is bounded, since f'(t) = b'(t) exp(b(t)).
Try $b(t) = sin(t^2)$.