Match List – I with List – II.
|
List - I |
List - II |
|
(A) $\frac{d}{d x}\left(\log _{e} x\right), x>0$ |
(I) $a^x \log _{e} a$ |
|
(B) $\frac{d}{d x}\left(x^{a}\right)$ |
(II) 0 |
|
(C) $\frac{d}{d x}\left(a^x\right), a>0$ |
(III) $\frac{1}{x}$ |
|
(D) $\frac{d}{d x}\left(a^{a}\right)$ |
(IV) $ax^{a-1}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
$\text{(A)}\; \frac{d}{dx}(\log_e x)=\frac{1}{x} \Rightarrow \text{(III)}$
$\text{(B)}\; \frac{d}{dx}(x^a)=ax^{a-1} \Rightarrow \text{(IV)}$
$\text{(C)}\; \frac{d}{dx}(a^x)=a^x \log_e a \Rightarrow \text{(I)}$
$\text{(D)}\; \frac{d}{dx}(a^a)=0 \Rightarrow \text{(II)}$
A–III,\; B–IV,\; C–I,\; D–II