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

If $x=\cos \theta$ and $y=\sin 5 \theta$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}$ is equal to (in $y$)

If $x = 3 \tan t$ and $y = 3 \sec t,$ then the value of $\frac{d^2y}{dx^2}$ at $t = \frac{\pi}{4}$ is

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

If $x=e^\theta(\sin \theta-\cos \theta)$ and $y=e^\theta(\sin \theta+\cos \theta)$,then $\frac{dy}{dx}$ at $\theta=\frac{\pi}{4}$ is:

Derivative of $\log (\sec \theta+\tan \theta)$ with respect to $\sec \theta$ at $\theta=\frac{\pi}{4}$ is