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What is the significance of the derivative of a probability density function of a continuous random variable ?

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In short? None. – Did Apr 28 '11 at 16:59
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No more significance than derivatives of any other functions. For example, you might want to use the derivative to find out where the density has a maximum. – Robert Israel Apr 28 '11 at 17:30
It's the instantaneous rate of change of probability density. </tautology> – anon Aug 26 '11 at 9:49

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It reduces Lebesgue-stielgies integral to the usual Lebesgue integral in computing,which is easier.

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+1 for spelling Lebesgue correctly, -1 for poor Stieltjes‌​. :) – Ilmari Karonen Nov 24 '11 at 13:14

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