Question

Find the second order derivatives of the following function tan⁻¹ x ?

Answer 1

We have,

\[y = \tan^{- 1} x\]

\[\text { Differentiating w . r . t . x, we get }\]

\[\frac{d y}{d x} = \frac{1}{1 + x^2}\]

\[\text { Differentiating again w . r . t . x, we get }\]

\[\frac{d^2 y}{d x^2} = - \left( 2x \right) \times \frac{1}{\left( 1 + x^2 \right)^2} = \frac{- 2x}{\left( 1 + x^2 \right)^2}\]