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Question
Find the second order derivatives of the following function tan−1 x ?
Solution
We have,
\[y = \tan^{- 1} x\]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = \frac{1}{1 + x^2}\]
\[\text { Differentiating again w . r . t . x, we get }\]
\[\frac{d^2 y}{d x^2} = - \left( 2x \right) \times \frac{1}{\left( 1 + x^2 \right)^2} = \frac{- 2x}{\left( 1 + x^2 \right)^2}\]
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