If $x=\cos 2 t+\log (\tan t)$ and $y=2 t+\cot 2 t$, then $\frac{d y}{d x}=$

The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is

If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2$, then $\tan \theta=$

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured in to the cone at the rate of $\frac{1}{\sqrt{3}} \mathrm{~m}^3 / \mathrm{min}$, then the rate ( $\mathrm{m} / \mathrm{min}$ ) at which the radius of the water level is increasing when the height of the water level is 3 m is