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.

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

Find the derivative of the following function.

${\left({\tan }^{-1}x\right)}^2$

Find the derivative of the following function.

${\sec }^{-1}\left(\mathrm{cosec}x\right)$

Find the derivative of the following function.

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