If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is

The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is

If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is

$\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is