Derivative of $\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right)$ with respect to $\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right)$ is

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

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$ then $x=$ ............

If $f(x)=\cos ^{-1}\left[\frac{1-(\log x)^2}{1+(\log x)^2}\right]$, then $f^{\prime}(e)=\ldots$