Mathematics · supplementary
Differentiability of fractional part function for JEE
Graphs of simple functions
Formula
\[\{x\}=x-[x],\quad \{x\}\text{ is continuous on }\mathbb R\setminus\mathbb Z,\text{ discontinuous at integers, and }\frac{d}{dx}\{x\}=1\text{ for }x\notin\mathbb Z\]
Variables: \(\{x\}\) is fractional part.
Conditions: Derivative not defined at integers.
Discontinuity and derivative of piecewise periodic functions.