Find the domain of differentiability of the following function:

$se{c}^{-1} x$

Find the domain of differentiability of the following function:

${\mathrm{cosec}}^{-1} x$

Find the domain of differentiability of the following function:

${\tan }^{-1} x$

Find the domain of differentiability of the following function:

${\cot }^{-1} x$

Find the derivative of the following function.

${\tan }^{-1}\left(x\sqrt{x}\right)$

Find the derivative of the following function.

${\cos }^{-1}3x$

Find the derivative of the following function.

$\sqrt{{\sin }^{-1}2x}$

Find the derivative of the following function.

$\sin \left({\tan }^{-1}x\right)$

Find the derivative of the following function.

$co{t}^{-1}\sqrt{x}$