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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 10

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Very short answers question 10

Answers (1)

Answer:

The answer of the given question is \frac{2}{1+x^{2}}

Given:

\text { Ify }=\sin ^{-1}\left[\frac{2 x}{1+x^{2}}\right] \text { write the value of } \frac{d y}{d x} \text { for } x>1 \text { . }

Hint:

\text { putting } x=\tan \theta

Solution:  

\begin{aligned} &y=\sin ^{-1}\left[\frac{2 x}{1+x^{2}}\right] \\\\ &y=\sin ^{-1}\left[\frac{2 \tan \theta}{1+\tan ^{2} \theta}\right] \end{aligned}

\begin{aligned} &y=\sin ^{-1} \sin 2 \theta \\\\ &y=2 \theta \\\\ &\Rightarrow y=2 \tan ^{-1} x \end{aligned}

\begin{aligned} &\Rightarrow \frac{d y}{d x}=2 \cdot \frac{1}{1+x^{2}} \\\\ &\Rightarrow \frac{d y}{d x}=\frac{2}{1+x^{2}} \end{aligned}

So the answer will be   \frac{2}{1+x^{2}}

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