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 $$f^{\prime}\left(\frac{\pi}{2}\right)=$$

If $$x=a \sec ^2 \theta$$ & $$y=a \tan ^2 \theta$$, then $$\frac{d^2 y}{d x^2}=$$

$$\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}$$, then $$\frac{d y}{d x}=$$