Choose the correct answer from the options given below :

Match List - I with List - II.

Choose the correct answer from the options given below :

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

If $x=\log_e t$ and $y=\dfrac{1}{t}$, then $\dfrac{d^2y}{dx^2}$ at $t=0.1$ is

Let $y = \cos(\sin x^2)$, then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{\pi}}{2}$ is equal to

Let a function $f(x)=\alpha+(\beta^2+5\beta+6)|x|+\gamma|x|^4$, where $\alpha, \beta$ and $\gamma$ are real number. Then the function $f(x)$ is differentiable at $x=0$ if

If $y = \sqrt{ax + b}$ then $y\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 =$