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 $\frac{d y}{d x}=$

If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{t}{2}\right)\right]$ then $\frac{d y}{d x}=$

The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ is