Match List-I with List-II.
| List-I | List-II | ||
| (A) | $f(x)=e^{2x}, $ then $f'(x)=$ | (I) | $2e^{2x}$ |
| (B) | If $g(x)=e^{logx^2},$ then $g'(x)= $ | (II) | $2x$ |
| (C) | If $h(x)=x^3,$ then $h'(x)=$ | (III) | $\frac{2}{x}$ |
| (D) | If $m(x)=logx^2$ then $m'(x) = $ | (IV) | $3x^2$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(I), (B)-(II), (C)-(IV), (D)-(III)
(A) $f(x)=e^{2x}$
$⇒f'(x)=2e^{2x}$
(B) $g(x)=e^{\log x^2}$
$⇒f'(x)=e^{\log x^2}.\frac{1}{x^2}×2x$
$=x^2×\frac{1}{x^2}×2x=2x$
(C) $h(x)=x^3$
$⇒h'(x)=3x^2$
(D) $m(x)=\log x^2$
$⇒m'(x)=\frac{1}{x^2}×2x=\frac{2}{x}$