Differentiate the following function with respect to $x$ :

${\cos }^{-1}\left\{\sqrt{\frac{1+x}{2}}\right\},-1<x<1$

Differentiate the following function with respect to $x$ :

${\sin }^{-1}\left\{\sqrt{\frac{1-x}{2}}\right\},0<x<1$

Differentiate the following function with respect to $x$ :

${\sin }^{-1}\left\{\sqrt{1-x^2}\right\},0<x<1$

Differentiate the following function with respect to $x$ :

${\tan }^{-1}\left\{\frac{x}{\sqrt{a^2-x^2}}\right\},-a<x<a$

Differentiate with respect to $x$

${\sin }^{-1}\left\{\frac{x}{\sqrt{x^2+a^2}}\right\}$

Differentiate the following function with respect to $x$.

${\sin }^{-1}\left(2x^2-1\right), 0<x<1$

Differentiate the following function with respect to $x$

${\sin }^{-1}\left(1-2x^2\right), 0<x<1$

Differentiate the following function with respect to $x$

${\cos }^{-1}\left\{\frac{x}{\sqrt{x^2+a^2}}\right\}$

Differentiate the following function with respect to $x$

${\sin }^{-1}\left\{\frac{\sin x+\cos x}{\sqrt{2}}\right\},-\frac{3\pi }{4}<x<\frac{\pi }{4}$