Match List I with List II

Choose the correct answer from the options given below :

A-III, B-IV, C-I, D-II

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)