Match List-I with List-II.
| List-I | List-II | ||
| (A) | If $f(x)=log(log\, x)$ then $f'(x)=$ | (I) | $\frac{1}{x\, log 2}$ |
| (B) | If $g(x)=e^{x^2},$ then $g'(x)=$ | (II) | $\frac{1}{x\, log x}$ |
| (C) | ,If $h(x)=\frac{2}{\sqrt{x}}, $ then$ h'(x)=$ | (III) | $e^{x^2}.2x$ |
| (D) | If $h(x)=log_2x,$ then $m'(x)=$ | (IV) | $-x^{-\frac{3}{2}}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
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) $h(x)=\log_2x$
$=\frac{\log x}{\log 2}$
$⇒h'(x)=\frac{1}{x\log 2}$