Differentiate the following w. r. t. x.y= ^2 (x^3 ) - Vidyadip

Question

Differentiate the following w. r. t. x.$y=\cot ^2\left(x^3\right)$

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Answer

$y=\cot ^2\left(x^3\right)$ Differentiate w. r.t. $x$ $ \begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}\left(\cot ^2\left(x^3\right)\right) \\ & =\frac{d}{d x}\left[\cot \left(x^3\right)\right]^2 \\ & =2 \cot \left(x^3\right) \frac{d}{d x}\left[\cot \left(x^3\right)\right] \\ & =2 \cot \left(x^3\right)\left[-\operatorname{cosec}^2\left(x^3\right)\right] \frac{d}{d x}\left(x^3\right) \\ & =-2 \cot \left(x^3\right) \operatorname{cosec}^2\left(x^3\right)\left(3 x^2\right) \\ \therefore \quad \frac{d y}{d x} & =-6 x^2 \cot \left(x^3\right) \operatorname{cosec}^2\left(x^3\right) \end{aligned} $

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