Match List-I with List-II.

Choose the correct answer from the options given below :

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

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

(A) $f(x)=\log(\log x)$

$f'(x)=\frac{1}{\log x}×\frac{1}{x}=\frac{1}{x\log x}$

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

$g'(x)=e^{x^2}.2x$

(C) $h(x)=\frac{2}{\sqrt{x}}$

$h'(x)=2×-\frac{1}{2}×x^{-3/2}=-x^{-3/2}$

(D) $h(x)=\log_2x$

$=\frac{\log x}{\log 2}$

$⇒h'(x)=\frac{1}{x\log 2}$