Match List-I with List-II:
|
List-I |
List-II |
|
(A) $\frac{5^x}{\log _e 5}$ |
(I) $5^x\left(\log _e 5\right)^2$ |
|
(B) $\log _e 5$ |
(II) $5^x \log _e 5$ |
|
(C) $5^x \log _e 5$ |
(III) $5^x$ |
|
(D) $5^x$ |
(IV) 0 |
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)
$(A)\;5^x\log_e5.$
$\frac{d}{dx}(5^x)=5^x\log_e5 \Rightarrow (A)\rightarrow(II).$
$(B)\;\log_e5.$
$\frac{d}{dx}(\log_e5)=0 \Rightarrow (B)\rightarrow(IV).$
$(C)\;5^x\log_e5.$
$\frac{d}{dx}(5^x\log_e5)=5^x(\log_e5)^2 \Rightarrow (C)\rightarrow(I).$
$(D)\;5^x.$
$\frac{d}{dx}(5^x)=5^x\log_e5 \Rightarrow (D)\rightarrow(II).$
$(A)\rightarrow(II),\;(B)\rightarrow(IV),\;(C)\rightarrow(I),\;(D)\rightarrow(II).$