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# What is the derivative of [ tanx] where [•] indicates greatest integer function?

Nandana
110 Points
4 years ago
hi,
It’s really fantastic question ! I’m so glad to answer this question
firstly , let us see what is greatest integer function ?
in Mathematics it is named as ‘Floor’ function ,
Floor (x) is the largest integer less than or equal to ‘x’
Ex: Floor(4.5) = 4
& one more thing Floor function follows the identity that
Floor (x+n) = n+ Floor(x) , where ‘n ‘ is an integer
now, coming to the question ,
d/dx(Floor(tanx)) = sec2(x) Floor(tan x),
but in walfram they give it as Floor’(tan x) but they didn’t show the plot
so , I’m also confused but I think they plot Dirac Delta functions infinitely by integrating them again we get same Floor function I think !