If $y = \sqrt{12^x(3x^2+2)}$, then $\dfrac{dy}{dx}$ will be

(consider $\log_e x = \log x$)

If $x^y = e^{x-y}$, then $\frac{dy}{dx} =$

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $y = (x+1)(x^2+1)(x^4+1)(x^8+1)$ then $\frac{dy}{dx}$ at $x = -1$ is

If $y = ax^{n+1} + bx^{-n}$, then $x^2 \dfrac{d^2y}{dx^2}$ is equal to

If $y = (\log_e x)^{\log_e x}$, then $\dfrac{dy}{dx}$ is equal to:

If $y = \log(\log x)$, then $\frac{d^2y}{dx^2}$ is equal to: (Consider $\log_e x = \log x$)