Question

Differentiate the following functions with respect to x

$2\sqrt{cot\left(x^2\right)}$

Answer 1

Let y = $2\sqrt{cot\left(x^2\right)}$

Differentiate both sides w.r.t. X,

$\frac{dy}{dx}=\frac{d}{dx}2(cont{x}^2{)}^{1/2}=2.\frac{1}{2}\{cot\left(x^2\right){\}}^{\frac{1}{2}-1}\frac{d}{dx}cot\left(x^2\right)$

[Using chain rule $\frac{d}{dx}f\left(g\right(x\left)\right)=f^{\prime }\left(x\right)\frac{d}{dx}g\left(x\right)$]

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

= $-\frac{cose{c}^2\left(x^2\right)2x}{\sqrt{cot\left(x^2\right)}}=\frac{-2xcose{c}^2\left(x^2\right)}{\sqrt{cot\left(x^2\right)}}$