Amit M Agarwal Solutions for Chapter: Continuity and Differentiability, Exercise 2: Work Book Exercise 5.2

If $f\left(x\right)={\sin }^{-1}\left(\frac{2x}{1+x^2}\right)$, then $f\left(x\right)$ is differentiable on

The set of points, where the function $f\left(x\right)=\sqrt{1-e^{-x^2}}$ is differentiable, is

If $f\left(x\right)=a\left|\sin x\right|+b{e}^{\left|x\right|}+c{\left|x\right|}^3$ and $f\left(x\right)$ is differentiable at $x=0$, then

The function $f\left(x\right)={\tan }^{-1}\left(\tan x\right)$ is

The number of points $\left(1,3\right)$ where $f\left(x\right)=a^{\left[x^2\right]}, a>1$, is not differentiable, is

Let $f\left(x\right)=\left[\left|x\right|\right]$, where $\left[·\right]$ denotes the greatest integer function, then $f^{\text{'}}\left(-1\right)$ is

Let $f\left(x+y\right)=f\left(x\right)f\left(y\right), \forall x, y\in R, f\left(5\right)=2$ and $f^{\text{'}}\left(0\right)=3$, then $f^{\text{'}}\left(5\right)$ equals

If $f\left(\frac{x}{y}\right)=\frac{f\left(x\right)}{f\left(y\right)}, \forall x, y\in R, y\ne 0$ and $f\left(t\right)=0$, if $t\ne 0$ and $f^{\text{'}}\left(1\right)=3$, then $f\left(x\right)$ is