For $N \in \mathbb{N}, \frac{\mathrm{~d}^{\mathrm{n}}}{\mathrm{d} x^{\mathrm{n}}}(\log x)=$

If $x=\operatorname{acos}^3 \theta y=\operatorname{asin}^3 \theta$

Then $\sqrt{1+\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2}=$

If $y=\sin ^2\left(\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

If $y=\mathrm{a}^x \cdot \mathrm{~b}^{2 x-1}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is equal to