Match List I with List II
| LIST I | LIST II | ||
| A. | $\frac{d}{dx}(a^x)$ | I. | 1 |
| B. | $\frac{d}{dx}(x^e)$ | II. | 2x |
| C. | $\frac{d}{dx}(e^{log_ex})$ | III. | $a^xlog_ea$ |
| D. | $\frac{d}{dx}(e^{2log_ex})$ | IV. | $ex^{e-1}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-III, B-IV, C-I, D-II
(A) $\frac{d}{dx}(a^x)=a^x\log_ea$ (III)
(B) $\frac{d}{dx}(x^e)=ex^{e-1}$ (IV)
(C) $\frac{d}{dx}(e^{\log_ex})=e^{log_ex}×\frac{1}{x}=x×\frac{1}{x}=1$ (I)
(D) $\frac{d}{dx}(e^{2\log_ex})=e^{2\log_ex}×\frac{2}{x}=x^2×\frac{2}{x}=2x$ (II)