If $x^2+y^2=t-\frac{1}{t}, x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$

If $f(x)=\frac{e^{-x} \sin x}{\log _e x}$ and $f^{\prime}(x)=f(x) \cdot g(x)$, then $g^{\prime}(e)=$

If $y=\frac{e^{\sin x}+\sinh ^3 x}{\cosh x-\tan x}$, then $y^{\prime}(0)=$

If $\frac{d}{d x}\left(\frac{2 x+1}{(x+1)^2(x-2)}\right)=\frac{A}{(x-2)^2}+\frac{B}{(x+1)^3}+\frac{C}{(x+1)^2}$, then $A+B+C=$