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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 38

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Answer:  \frac{1}{\left(1+x^{2}\right) \tan ^{-1}(x)}

Hint: You must know about the rules of solving derivative of logarithm and Inverse trigonometric function.

Given:  \log \left(\tan ^{-1} x\right)


Let  y=\log \left(\tan ^{-1} x\right)

Differentiate with respect to x,

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

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