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How can prove or disprove that bounded smooth functions have a bounded derivative ? For example cosinx is bounded and smooth and has bounded derivative . I can’t think of a proof to show that the claim is true ,nor can I think of a counterexample. Even a hint would be very useful .

user3503589
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    https://math.stackexchange.com/questions/257584/can-the-graph-of-a-bounded-function-ever-have-an-unbounded-derivative – Thomas Fjærvik Mar 04 '19 at 23:45
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    Since you're requiring your function to be smooth and bounded, consider a function that has bounded oscillations. Can you make it so that these oscillations grow more and more (are unbounded)? – Chris Mar 05 '19 at 00:57

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