Find the second order derivatives of the following functions: y= … - Vidyadip

Question

Find the second order derivatives of the following functions:
$\text{y}=\tan^{-1}\text{x}$

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Answer

We have,
$\text{y}=\tan^{-1}\text{x}$
differentiating w.r.t.x, we get
$\frac{\text{dy}}{\text{dx}}=\frac{1}{1+\text{x}^2}$
differentiating w.r.t.x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=-(2\text{x})\times\frac{1}{(1+\text{x}^2)^2}$
$=\frac{-2\text{x}}{(1+\text{x}^2)^2}$

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