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  • Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 42

Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 42

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of cosec-1x

Given:

y=\left(\operatorname{cosec}^{-1} x\right), x>1 , \text { prove } x\left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+\left(2 x^{2}-1\right) \frac{d y}{d x}=0

Solution:

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

        \begin{aligned} &\text { Again differentiating }\\ &x \sqrt{x^{2}-1} \frac{d^{2} y}{d x^{2}}+\sqrt{x^{2}-1} \frac{d y}{d x}+x \cdot \frac{2 x}{2 \sqrt{x^{2}-1}} \frac{d y}{d x}=0\\ &x\left(x^{2}-1\right) \frac{d^{2} y}{d x^{2}}+\left(2 x^{2}-1\right) \frac{d y}{d x}=0 \end{aligned}

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Gurleen Kaur

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