# Domain Differentiation question

by Bachelier
Tags: differentiation, domain
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,489 The function, f(x)= 0 if x< 0 and rational or $x> 2\pi$ and rational, f(x)= 1 if x< 0 and irrational or $x> 2\pi$ and irrational, f(x)= 3 for all other x, is differentiable for all x in $[0, 2\pi]$ but not differentiable for any other f. Since it does not have a derivative on $[-\pi, 0]$, no, its derivative cannot be integegrated there!