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  • Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 16

Explain solution RD Sharma class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Question question 16

Answers (1)

Answer:

                (a)

Hint:

We must have known about the derivative of trigonometric function like  \sin^{-1}x .

Given:

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

Explanation:

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

Differentiate with respect to x

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

Again differentiate with respect to x

                \frac{d^{2} y}{d x^{2}}=\frac{2 \frac{1}{\sqrt{1-x^{2}}} \times \sqrt{1-x^{2}}}{\left(1-x^{2}\right)}-\sin ^{-1}\left(\frac{x-2 x}{2 \sqrt{1-x^{2}}}\right)

                \left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}=2\left[1+\frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}}\right] \\

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

                \begin{gathered} \left(1-x^{2}\right) y_{2}=2+x y_{1} \end{gathered}

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