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Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  18

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Answer: \frac{3}{\sqrt{1-x^{2}}}

Hint: \text { put } x=\sin \theta

Given: y=\sin ^{-1}\left(3 x-4 x^{3}\right)

Solution:  By putting x=\sin \theta \text { in } \mathrm{y}

\begin{aligned} &y=\sin ^{-1}(3 \sin \theta-4 \sin \theta) \\\\ &y=\sin ^{-1}(\sin 3 \theta) \end{aligned}

    \begin{aligned} &=3 \theta \\\\ &=3 \sin ^{-1} x \end{aligned}

\frac{d y}{d x}=\frac{3}{\sqrt{1-x^{2}}}


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