If $x=\sin \theta, y=\sin ^3 \theta$ then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{2}$ is ............

If $x^y=e^{x-y}$, then $\frac{d y}{d x}$ at $x=1$ is ...........

Derivative of $\log _{e^2}(\log x)$ with respect to $x$ is

If $x=\sqrt{a^{\sin ^{-1} t}}, y=\sqrt{a^{\cos ^{-1} t}}$, then $\frac{d y}{d x}=\ldots .$.