If $\sin^{-1} x + \sin^{-1} y = \frac{2\pi}{3}$,then $\cos^{-1} x + \cos^{-1} y = $

Considering only the principal values of the inverse trigonometric functions,the value of $\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^2}+\tan ^{-1} \frac{\sqrt{2}}{\pi}$ is:

If $f(x) = \tan^{-1}\left\{ \frac{\log(e/x^2)}{\log(ex^2)} \right\} + \tan^{-1}\left( \frac{3 + 2\log x}{1 - 6\log x} \right)$,then $\frac{d^n y}{dx^n}$ is $(n \ge 1)$.

If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$,then the value of $x$ is

$\sin \left[3 \sin ^{-1}(0.4)\right] = \ldots$

If $y = \tan^{-1} \left( \frac{x^{1/3} + a^{1/3}}{1 - x^{1/3}a^{1/3}} \right)$,then $\frac{dy}{dx} = $