Match List-I with List-II

Choose the correct answer from the options given below :

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

The correct answer is option (4) → (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(A) $y=\log(\sin x)$

$\frac{dy}{dx}=\cot x⇒\frac{d^2y}{dx^2}=-cosec^2x$ (IV)

(B) $y=e^{(1+\log x)}$

$⇒\log y=1+\log x$

$\log y=\log ex⇒y=ex$

so $\frac{d^2y}{dx^2}=0$ (III)

(C) $y=\log x⇒\frac{d^2y}{dx^2}=\frac{-1}{x^2}$ (I)

(D) $y=x^2+4x-1⇒\frac{d^2y}{dx^2}=2$ (II)