Question

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

Answer 1

$2\sqrt{\cot x^2}$

$=\frac{2}{2\sqrt{\cot x^2}}(-{\csc }^2{x}^2)\left(2x\right)=\frac{-4x{\csc }^2{x}^2}{2\sqrt{\cot x^2}}$

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

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

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