CUET Mathematics 2023 15 June Shift 2 PYQs

If $\sin y = x \cos(a + y)$, then $\frac{dy}{dx}$ is equal to

If $x = e^{y + e^{y + e^{y + \ldots \infty}}}$, $x > 0$, then $\frac{dy}{dx}$ is equal to

If $y = \log_e\left(\frac{e^2}{x^2}\right)$ for $x \neq 0$, then $\frac{d^2y}{dx^2}$ equals