The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is

If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $

If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $