For $x<0, \frac{d}{d x}\left[|x|^x\right]=$

If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is

If $y=f(x)$ is a thrice differentiable function and a bijection, then $\frac{d^2 x}{d y^2}\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}=$

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