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

$\sqrt{\tan \sqrt{x}}$

Differentiate w.r.t. $x$

 ${\cot }^3\left[\log \left(x^3\right)\right]$

Differentiate w.r.t. $x$

 $5^{{\sin }^{3}x+3}$

Differentiate w.r.t. $x$

 $cosec\left(\sqrt{\cos x}\right)$

Differentiate w.r.t. $x$

 $\log \left[\cos \left(x^3-5\right)\right]$

Differentiate w.r.t. $x$

 $e^{3{\sin }^{2}x-2{\cos }^{2}x}$

Differentiate w.r.t. $x$

 $e^{\log \left[(\log x{)}^2-\log x^2\right]}$

Differentiate w.r.t. $x$

 $\tan \left[\cos \right(\sin x\left)\right]$

Differentiate w.r.t. $x$

 $\sec \left[\tan \left(x^4+4\right)\right]$