If $\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2$,then $\frac{dy}{dx}$ is equal to

$f(x)$ and $g(x)$ are two differentiable functions on $[0, 2]$ such that $f''(x) - g''(x) = 0$,$f'(1) = 2$,$g'(1) = 4$,$f(2) = 3$,and $g(2) = 9$. Then $f(x) - g(x)$ at $x = 3/2$ is:

If $\sin^2 x + 2\cos y + xy = 0$,then $\frac{dy}{dx} = $

If $x^{\frac{2}{5}}+y^{\frac{2}{5}}=a^{\frac{2}{5}}$,then $\frac{dy}{dx} = $

If $y = \log_y x$,then $\frac{dy}{dx}$ is equal to

If $y$ is a function of $x$ and $\log (x+y)=2xy$,then the value of $y^{\prime}(0)$ is