# Differentiation wrt a Floor Division

I have been racking my brain on how i should go about resolving:

$$\frac{d( n (\frac{g}{n} - \lfloor\frac{g}{n}\rfloor))}{d \lfloor\frac{g}{n}\rfloor}$$ For this case replace $${\lfloor\frac{g}{n}\rfloor}$$ as $${f(\frac{g}{n})}$$ (assume it is continuous)

How can I go about this, when this whole thing seems intertwined. I'm not looking for a partial; but even if I was, I wouldn't know where to start.

{ The original differential was $$\frac{d mod(g,n)}{d g//n}$$ where

mod(g,n) ==modulus of g wrt n

g//n == floor(g/n)}

• I can't think of an interpretation of the notation where taking derivatives makes sense. None of these functions are continuous, and the functions in the denominator are piecewise constant. – Greg Martin Mar 30 at 7:28