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Asked • 03/14/19

Is the derivative function typically "worse" than the original function?

For instance, the absolute value function is defined and continuous on the whole real line, but its derivative behaves like a step function with a jump-discontinuity. For some nice functions, though, such as $e^x$ or $\\sin(x)$, the derivatives of course are no "worse" than the original function. Can I say something that is *typical* of the derivative? Is it typically not as nice as the original function?

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