Question

Differentiate:
$y=2\sqrt{\cot x}$

Answer 1

$y=2\sqrt{cotx}$

$\frac{y}{2}=\sqrt{\cot x}$

Squaring both sides, we have

$\frac{y^2}{4}=cotx$

$\frac{2y}{4}\frac{dy}{dx}=-cs{c}^{2}x$

$\Rightarrow \frac{dy}{dx}=\frac{2}{y}(-cs{c}^{2}x)$

$\Rightarrow \frac{dy}{dx}=-\frac{2cs{c}^{2}x}{2sqrtcotx}$

$\Rightarrow \frac{dy}{dx}=-\frac{\left(\frac{1}{si{n}^{2}x}\right)}{sqrt\frac{\cos x}{sinx}}=-\frac{1}{sinx\sqrt{sinxcosx}}=-\csc x\sqrt{cscxsecx}$

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