If $\cot[f(x)] = \dfrac{3x - x^3}{1 - 3x^2}$ and $\sin[g(x)] = \dfrac{1 - x^2}{1 + x^2}$, then $\lim\limits_{x \to t}\dfrac{f(x) - f(t)}{g(x) - g(t)} = \ldots$

If $y = \cos^{-1}\left(\dfrac{1 - 4^x}{1 + 4^x}\right)$, then $\dfrac{dy}{dx}$ at $x = 1$ is

If $y = \tan^{-1}\left[\dfrac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}}\right]$ , then $\dfrac{dy}{dx} =$

The derivative of $\log_8(\log_5 x)$ w. r. t. $x$ is