If $(\mathrm{a}+\mathrm{b} x) \mathrm{e}^{\frac{y}{x}}=x$, then $x^3 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}$ is equal to

If $x=\log \mathrm{t}, \mathrm{t}>0$ and $y=\frac{1}{\mathrm{t}}$ then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$

If $y=\frac{\mathrm{K}^{\cos ^{-1} x}}{1+\mathrm{K}^{\cos ^{-1} x}}$ and $\mathrm{t}=\mathrm{K}^{\cos ^{-1} x}$, then $\frac{\mathrm{d} y}{\mathrm{dt}}=$

The complex numbers $\sin x+i \cos 2 x$ and $\cos x$ - $\mathrm{i} \sin 2 x,(\mathrm{i}=\sqrt{-1})$ are conjugate to each other for,