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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Find the second order derivatives of the function given in Exercise:
$\tan^{-1}\text{x}$
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Answer

Let $\text{y}=\tan^{-1}\text{x}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{1}{1+\text{x}^2}$
and $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{(1+\text{x}^2).0-1.2\text{x}}{(1+\text{x}^2)^2}=-\frac{2\text{x}}{(1+\text{x}^2)^2}$

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