If y=tan ^-1 x then dy/dx at y=(π)/3 is equal to:

The correct answer is Option (4) → $\frac{1}{4}$

$\frac{dy}{dx}=\frac{1}{1+x^2}⇒\left.\frac{dy}{dx}\right]_{at\,y=\frac{\pi}{3}}$

$\tan^{-1}x=\frac{\pi}{3}⇒x=\sqrt{3}$

$\frac{dy}{dx}=\frac{1}{1+{\sqrt{3}}^2}$

$=\frac{1}{4}$