If $y = x^3\log(3x^2+6)$, then $\dfrac{dy}{dx} =$

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $y = t - \frac{1}{t}$ and $x = t + \frac{1}{t}$, then $\frac{dy}{dx}$ is equal to

If $xy + \frac{x^2}{y} = x^3y + y$, then $\frac{dy}{dx}$ is equal to

The second order derivative of which of the following functions is $5^{\mathrm{x}}$ ?

If $t=e^{2 x}$ and $y=\log _{e} t^{2}$, then $\frac{d^{2} y}{d x^{2}}$ is :

$\frac{d^2}{dx^2} \left\{ \det \begin{bmatrix} x^3 & x \\ 2 & e^x \end{bmatrix} \right\}$ equals