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  • Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 20 maths

Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 20 maths

Answers (1)

Answer:

        0

Hint:

You must know about derivative of sin-1 x

Given:

I\! f y=(sin^{-1}x)^{2} \; \; Prove\: that\: \: (1-x^{2})y_{2}-xy_{1}-2=0

Solution:

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

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

        \begin{aligned} &\frac{d^{2} y}{d x^{2}}=\frac{2\left(1+\frac{x \sin ^{-1} x}{\sqrt{1-x^{2}}}\right)}{1-x^{2}} \\ &\left(1-x^{2}\right) y_{2}=\frac{2+2 x \sin ^{-1} x}{\sqrt{1-x^{2}}} \\ &\left(1-x^{2}\right) y_{2}-y_{1} x-2=0 \end{aligned}

Hence proved

Posted by

Gurleen Kaur

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