Differentiation of Different Type of Functions

Differentiate the following w.r.t $x:$

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

Differentiate the following function w.r.t.$x$: ${\tan }^{-1}\left(\frac{5-x}{6x^2-5x-3}\right)$.

Differentiate the following function w.r.t.$x$: ${\tan }^{-1}\left(\frac{a\cos x-b\sin x}{b\cos x+a\sin x}\right)$.

Differentiate the following function w.r.t. $x$: ${\tan }^{-1}\left(\frac{7x}{1-12x^2}\right)$.

Differentiate the following function w.r.t. $x$: ${\tan }^{-1}\left(\frac{5ax}{a^2-6x^2}\right)$.

Differentiate the following function w.r.t. $x$: ${\tan }^{-1}\left(\frac{x-a}{x+a}\right)$.

Differentiate the following function w.r.t.$x$: ${\tan }^{-1}\left(\frac{\sqrt{x}}{1+20x}\right)$.

Differentiate the following function w.r.t.$x$: ${\tan }^{-1}\left(\frac{6x}{1-8x^2}\right)$.

Differentiate the following function w.r.t.$x$: ${\tan }^{-1}\left(\frac{2^{x+1}}{1-4^x}\right)$.

Differentiate the following function w.r.t $x$: ${\tan }^{-1}\left(\frac{3a^{2}x-x^3}{a^3-3a{x}^2}\right)$.

Differentiate the following function w.r.t $x$: ${\tan }^{-1}\sqrt{\frac{a-x}{a+x}}$.

Differentiate the following functions w.r.t. $x$

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

Differentiate the following function w.r.t.$x$: ${\cos }^{-1}\left(\frac{a^{-x}-a^x}{a^{-x}+a^x}\right)$.

Differentiate the following functions w.r.t. $x$

${\sin }^2\left({\cot }^{-1}\sqrt{\frac{1+x}{1-x}}\right)$

Differentiate the following function w.r.t.$x$: ${\sin }^{-1}\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right)$.

Differentiate the following function w.r.t $x$: ${\sin }^{-1}\left(\frac{1-25x^2}{1+25x^2}\right)$.

Differentiate the following function w.r.t.$x$: ${\sec }^{-1}\left(\frac{1+{\mathrm{e}}^{2\sqrt{x}}}{2e^{\sqrt{x}}}\right)$.

Differentiate the following function w.r.t.$x$: ${\sin }^{-1}\left(\frac{x}{\sqrt{x^2+a^2}}\right)$.

Differentiate the following functions w.r.t. $x$

${\cos }^{-1}\frac{\sqrt{3}\cos x+\sin x}{2}$

Differentiate the following functions w.r.t. $x$

${\cos }^{-1}\left(\frac{\cos x+\sin x}{\sqrt{2}}\right)$