Differentiate the functions with respect to x. 2 (x^ 2 ) - Vidyadip

Question

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

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Answer

$\text{Let y} =2\sqrt{\cot(\text{x}^{2})}$
$\therefore \frac{\text{dy}}{\text{dx}} =2\frac{1}{2}\left\{\cot(\text{x}^{2})^\frac{{-1}}{{2}}\right\}.\frac{\text{d}}{\text{dx}}\cot(\text{x}^{2})$
$\frac{1}{\sqrt{\cot(\text{x})^{2}}}.\left\{-\text{cosec}\text{(x}^{2})\right\}\frac{\text{d}}{\text{dx}}\text{x}^{2}$
$\frac{1}{\sqrt{\cot(\text{x})^{2}}}.\left\{-\text{cosec}\text{(x}^{2})\right\}(2\text{x})=\frac{-2\text{x cosec}(\text{x}^{2})}{\sqrt{\cot(\text{x}^{2})}}$

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