Question

Differentiate the function with respect to $x$
$2\sqrt{\cot \left(x^2\right)}$

Answer 1

$\frac{d}{dx}\left[2\sqrt{\cot \left(x^2\right)}\right]$

$=2.\frac{1}{2\sqrt{\cot \left(x^2\right)}}\times \frac{d}{dx}\left[\cot \right(x^2\left)\right]$

$=\sqrt{\frac{\sin \left(x^2\right)}{\cos \left(x^2\right)}}\times -cose{c}^2\left(x^2\right)\times \frac{d}{dx}\left(x^2\right)$

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

$=\frac{-2x}{\sqrt{\cos x^2}\sqrt{\sin x^2}\sin x^2}$

$=\frac{-2\sqrt{2}x}{\sqrt{2\sin x^2\cos x^2}\sin x^2}$

$=\frac{-2\sqrt{2}x}{\sin x^2\sqrt{\sin \left(2x^2\right)}}$