We know differentiability implies continuity, and in 2 independent variables cases both partial derivatives(adsbygoogle = window.adsbygoogle || []).push({}); fand_{x}fmust be continuous functions in order for the primary function_{y}f(x,y)to be defined as differentiable.

However in the case of 1 independent variable, is it possible for a function f(x) to be differentiable throughout an interval R but it's derivative f ' (x) is not continuous?

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# Differentiability implies continuous derivative?

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