Question

If $f\left(x\right)=si{n}^{-1}\left(sinx\right)+co{s}^{-1}\left(sinx\right)$ and $\varphi \left(x\right)=f\left(f\right(f\left(x\right)\left)\right)$, then ${\varphi }^{\prime }\left(x\right)$ is equal to

• A. 1
• B. sin x
• C. None of these

Answer 1

$f\left(x\right)=\frac{\pi }{2}$ (a constant function)
$\Rightarrow {\varphi }^{\prime }\left(x\right)=0$