The function $x^x ; x>0$ is strictly increasing at

The maximum volume of the right circular cone with slant height 6 units is

If $f(x)=x e^{x(1-x)}$, then $f(x)$ is

If $$u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$ and $$v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, then $$\frac{d u}{d v}$$ is