When I plot $$f(x) =\frac{\arctan(\tan(2\pi x))}{2\pi}$$ in WolframAlpha, it gives me an expected sawtooth wave.
When I try the derivative of this function, it gives me $1$. I expect that since there is a discontinuity in this function at $(2k+1)\pi/4$, derivative is not defined in those points in the traditional sense. But I am looking for a derivative expression that can include dirac-delta function. For example, when I try finding the derivative of $\text{Heaviside}(x)$, it gives me a result of $\delta(x)$. I understand that dirac-delta is not a function in strict sense. Can anyone point me towards a solution or generally how to approach this?