Match List-I with List-II

Choose the correct answer from the options given below :

(A)-(IV), (B)-(III),(C)-(II), (D)-(I)

The correct answer is Option (2) → (A)-(IV), (B)-(III),(C)-(II), (D)-(I)

(A) $y=\log e^x=x\log e=x$

$→y'=1$ and $y''=0$

(B) $y=e^{2x}$

$⇒\frac{dy}{dx}=2e^{2x}⇒\frac{d^2y}{dx^2}=4e^{2x}$

(C) $y=\sqrt{x}$

$⇒\frac{dy}{dx}=\frac{1}{2\sqrt{x}}⇒\frac{d^2y}{dx^2}=\frac{-1}{4x\sqrt{x}}$

(D) $y=e^{-x}$

$⇒\frac{dy}{dx}=-e^{-x}⇒\frac{d^2y}{dx^2}=e^{-x}=\frac{1}{e^x}$