Question

$Letf\left(x\right)=x-\left[x\right],x\in R$. $Then{f}^{\prime }\left(\frac{1}{3}\right)=...$

Answer 1

Given:
$f\left(x\right)=x-\left[x\right],x\in R$

We know that, $For0\le x<1,\left[x\right]=0.$

$\therefore f\left(x\right)=x-0$

$\Rightarrow f\left(x\right)=x$

The differentiation of the given function for

$x\in [0,1)$

$f^{\prime }\left(x\right)=\frac{d}{dx}\left(x\right)$


$\Rightarrow f^{\prime }\left(x\right)=1$

$\therefore f^{\prime }\left(\frac{1}{3}\right)=1$