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Abstract
In the study of differential and integral calculus and especially in real analysis, Dini derivatives are a type of generalization of derivatives, introduced by Ulisse Dini (1845 – 1918), to study continuous functions that are not differentiable. In this work, the definition of the four Dini derivatives is presented and their most important properties are given. Monotone functions are also characterized by the sign of their four Dini derivatives and it is proved that the set of points where the function is not differentiable has measure zero. Finally, a version of the fundamental theorem of calculus is presented, but now using the Dini derivative.
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