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

Differentiate $\sin ^2 x$ with respect to $\cos ^2 x$.

If $y=a \sin ^3 t$ and $x=a \cos ^3 t$,then $\frac{d y}{d x}$ at $t=\frac{3 \pi}{4}$ is

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

If $x = \sin \theta$ and $y = \sin^3 \theta$,then the value of $\frac{d^2 y}{d x^2}$ at $\theta = \frac{\pi}{6}$ is: