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

If $x^3+y^3=3axy$,then at $\left(\frac{3a}{2}, \frac{3a}{2}\right)$ the value of $3ay^{\prime \prime}+40$ is

The focal length of a mirror is given by $\frac{2}{f} = \frac{1}{v} - \frac{1}{u}$. In finding the values of $u$ and $v$,the errors are equal to $p$. Then,the relative error in $f$ is

$If \frac{x}{x-y} = \log \left(\frac{a}{x-y}\right)$,then $\frac{dy}{dx} =$

If $x > 0$ and $x^y = e^{x-y}$,then $\frac{dy}{dx}$ is equal to

If $x \cdot \log _{e}(\log _{e} x)-x^2+y^2=4$ and $y>0$,then $\frac{dy}{dx}$ at $x=e$ is