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  • Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.8 question 2

Provide solution for RD Sharma maths class 12 chapter Differentiation exercise 10.8 question 2

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Answer: 2x

Hint: Let u=\log \left(1+x^{2}\right), v=\tan ^{-1} x

            \frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}}
 

Given:   \log \left(1+x^{2}\right) \text { w.r.t } \tan ^{-1} x

Explanation:

\text { Let } u=\log \left(1+x^{2}\right), v=\tan ^{-1} x

\begin{aligned} &\frac{d u}{d x}=\frac{1}{1+x^{2}} \times 2 x=\frac{2 x}{1+x^{2}} \\\\ &\frac{d v}{d x}=\frac{1}{1+x^{2}} \end{aligned}

\frac{d u}{d v}=\frac{\frac{d u}{d x}}{\frac{d v}{d x}}=\frac{\frac{2 x}{1+x^{2}}}{\frac{1}{1+x^{2}}}=2 x

 

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