If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is

If $$y=2 x^{n+1}+\frac{3}{x^n}$$, then $$x^2 \frac{d^{2 y}}{d x^2}$$ is

If $$(x e)^y=e^y$$, then $$\frac{d y}{d x}$$ is

If $$[x]$$ represents the greatest integer function and $$f(x)=x-[x]-\cos x$$, then $$f^{\prime}\left(\frac{\pi}{2}\right)=$$