Differentiation — Maths STD 12 Science — Question

\begin{array}{ll}

\text { Let } y=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right) \\

& \text { Put } x=\tan \theta \therefore \theta=\tan ^{-1} x \\

\therefore \quad & y=\sin ^{-1}\left(\frac{2 \tan \theta}{1+\tan ^2 \theta}\right) \\

& y=\sin ^{-1}(\sin 2 \theta)=2 \theta \\

\therefore \quad & y=2 \tan ^{-1} x

\end{array}

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Differentiate $w . r . t . x$.

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\begin{aligned}

\frac{d y}{d x} & =2 \frac{d}{d x}\left(\tan ^{-1} x\right) \\

\therefore \quad \frac{d y}{d x} & =\frac{2}{1+x^2}

\end{aligned}

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