Mathematics - Vector Question with Solution | TestHub

number of points where $|\mathrm{f}(|\mathrm{x}|)|$ is non derivable is 0

$\mathrm{sgn}(\mathrm{f}(\mathrm{x}))$ is discontinuous at $\mathrm{x}=1$.

derivative of $f(x)$ with respect to ${\sin }^{-1}\left(\frac{2x}{1+x^2}\right)$ at $x=\sqrt{3}$ is -4 .

${\lim }_{x\to 0^{+}}{\left(\frac{\sqrt{3}f(x)}{x}\right)}^x=1$.