Match List I with List II LIST I LIST II A. $\frac{d}{dx}(a^x)$ I. 0 B. $\frac{d}{dx}(x^a)$ II. $x^x(1+log_ex)$ C. $\frac{d}{dx}(a^a)$ III. $ax^{a-1}$ D. $\frac{d}{dx}(x^x)$ IV. $a^xlog_ea$ Choose the correct answer from the options given below :

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

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

The correct answer is Option (4) → A-IV, B-III, C-I, D-II (A) $\frac{d}{dx}(a^x)=a^x\log a$ (IV) (B) $\frac{d}{dx}(x^a)=ax^{a-1}$ (III) (C) $\frac{d}{dx}(a^a)=0$ (I) (D) $\frac{d}{dx}(x^x)=x^x(1+\log x)$ (II)