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explain solution RD Sharma class 12 chapter Differentiation exercise 10.2 question 35 maths

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Answer:\frac{2 \cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}}

Hint: You must know about the rules of solving derivative of Trigonometry and Inverse trigonometric function

Given:  \sin \left(2 \sin ^{-1} x\right)

Solution:

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

Differentiate with respect to x,

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x}\left[\sin \left(2 \sin ^{-1} x\right)\right] \\\\ &\frac{d y}{d x}=\cos \left(2 \sin ^{-1} x\right) \frac{d}{d x}\left(2 \sin ^{-1} x\right) \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\cos \left(2 \sin ^{-1} x\right) \times 2 \times \frac{1}{\sqrt{1-x^{2}}} \\\\ &\frac{d y}{d x}=\frac{2 \cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}} \end{aligned}

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