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  • Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 28 maths

Explain solution RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 28 maths

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of logarithm and tangent inverse x

Given:

y=\left(\tan ^{-1} x\right)^{2}, \text { show }\left(1+x^{2}\right)^{2} y_{2}+2 x\left(1+x^{2}\right) y_{1}=2

Solution:

        \begin{aligned} &y=\left(\tan ^{-1} x\right)^{2}\\ &\text { Differentiate the equation w.r.t } x\\ &\frac{d y}{d x}=2 \tan ^{-1} x \cdot \frac{1}{1+x^{2}}\\ &\left(1+x^{2}\right) \frac{d y}{d x}=2 \tan ^{-1} x \end{aligned}

        \begin{aligned} &\text { Differentiate again }\\ &\left(1+x^{2}\right) \frac{d^{2} y}{d x^{2}}+(2 x) \frac{d y}{d x}=\frac{2}{1+x^{2}}\\ &\left(1+x^{2}\right)^{2} \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}\left(1+x^{2}\right)(2 x)=2\\ or\\ &\left(1+x^{2}\right)^{2} y_{2}+2 x\left(1+x^{2}\right) y_{1}=2 \end{aligned}

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Gurleen Kaur

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