Diffrentiate the following w. r. t. x. ^ -1 [ (e^ x 2 ) ] - Vidyadip

Question

Diffrentiate the following w. r. t. x.

$\cot ^{-1}\left[\cot \left(e^{ x 2}\right)\right]$

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Answer

Let $y=\cot ^{-1}\left[\cot \left( e ^{ x 2}\right)\right]= e ^{ x 2}$

Differentiating w.r.t. $x$, we get

$\frac{d y}{d x}=\frac{d}{d x}\left(e^{x^2}\right)=e^{x^2} \cdot \frac{d}{d x}\left(x^2\right)$

$=e^{x^2} \times 2 x=2 x e^{x^2}$

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