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  • Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 4 maths

Explain solution RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 4 maths

Answers (1)

Answer:

        \frac{x}{\sqrt{1+x^{2}}}

Hint:

        Differentiate the function w.r.t x

Given:

        \sec \left(\tan ^{-1} x\right)

Solution:  

        \begin{aligned} &y=\sec \left(\tan ^{-1} x\right) \\\\ &\frac{d y}{d x}=\sec \left(\tan ^{-1} x\right) \tan \left(\tan ^{-1} x\right) \times \frac{d}{d x}\left(\tan ^{-1} x\right) \end{aligned}

               \begin{aligned} &=\sec \left(\tan ^{-1} x\right) \tan \left(\tan ^{-1} x\right) \times \frac{1}{\sqrt{1+x^{2}}} \\\\ &=y \tan \left(\tan ^{-1} x\right) \times \frac{1}{\sqrt{1+x^{2}}} \end{aligned}

               =y\left(\frac{x}{\sqrt{1+x^{2}}}\right) \; \; \; \; \; \; \quad\left[\tan \left(\tan ^{-1} x\right)=x\right]

This is the equation of differential equation which have co-efficient= \left(\frac{x}{\sqrt{1+x^{2}}}\right)

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