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

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

Answers (1)

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)

Solution:

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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