If $u=\cos ^3 x$ and $v=\sin ^3 x$,then $\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}}$ is equal to

If $y=4 \cos ^3(t)$ and $x=4 \sin ^3(t)$,then $\frac{d y}{d x}$ is equal to

If $x$ and $y$ are connected parametrically by the equations,without eliminating the parameter,find $\frac{d y}{d x}$:
$x = \frac{\sin^3 t}{\sqrt{\cos 2t}}, y = \frac{\cos^3 t}{\sqrt{\cos 2t}}$

Find $\frac{dy}{dx}$,if $x = at^2$ and $y = 2at$.

If $\cos x = \frac{1}{\sqrt{1 + t^2}}$ and $\sin y = \frac{t}{\sqrt{1 + t^2}}$,then $\frac{dy}{dx} = $

If $x = \sin 2\theta \cos 3\theta$ and $y = \sin 3\theta \cos 2\theta$, then find $\frac{dy}{dx}$.