Question

Find the second order derivative of the following function:
${\tan }^{-1}x$

Answer 1

Let $y=ta{n}^{-1}x.$ Then,
$\frac{dy}{dx}=\frac{1}{1+x^2}=(1+x^2{)}^{-1}\Rightarrow \frac{d^{2}y}{d{x}^2}=-(1+x^2{)}^{-2}\frac{d}{dx}(1+x^2)=-\frac{2x}{(1+x^2{)}^2}$