The derivative of $\sin(x^{3})$ with respect to $\cos(x^{3})$ is

If $x=a(t-\sin t)$ and $y=a(1+\cos t)$,then $\frac{d^2 y}{d x^2}=$

If $\sin x = \frac{2t}{1+t^2}$ and $\tan y = \frac{2t}{1-t^2}$,then $\frac{dy}{dx}$ is equal to

If $x = a(t + \sin t)$ and $y = a(1 - \cos t)$,then $\frac{dy}{dx}$ equals

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{dy}{dx}$ for $x = \cos \theta - \cos 2\theta$ and $y = \sin \theta - \sin 2\theta$.

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{dy}{dx}$ for $x=4t$ and $y=\frac{4}{t}$.