If $f$ is differentiable in $(0, 6)$ and $f'(4) = 5$,then $\lim_{x \to 2} \frac{f(4) - f(x^2)}{2 - x} = $

The derivative of $\tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{x}\right)$ with respect to $\tan ^{-1}\left(\frac{2 x \sqrt{1-x^{2}}}{1-2 x^{2}}\right)$ at $x=\frac{1}{2}$ is

The derivative of $\operatorname{Sec}^{-1}\left(\frac{1}{2x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ is

For $-\frac{\pi}{2} < x < \frac{3 \pi}{2}$, the value of $\frac{d}{d x}\left\{\tan ^{-1} \frac{\cos x}{1+\sin x}\right\}$ is equal to

If $y = \sin^{-1}\left(\frac{3x}{2} - \frac{x^3}{2}\right)$,then $\frac{dy}{dx}$ is equal to

If $y=\tan ^{-1}\left(\frac{5 x+1}{3-x-6 x^2}\right)$,then $\frac{d y}{d x}=$