(A) $\frac{d}{d x} a^x=\frac{a^x}{\log _{e} a}$
(B) $\frac{d}{d x} e^{ax}=a e^{ax}$
(C) $\frac{d}{d x} x^x=x . x^{x-1}$
(D) $\frac{d}{d x} x^{a}=a x^{a-1}$
(E) $\frac{d}{d x} a^{a}=0$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
(A) $\frac{d}{d x} a^x=\frac{a^x}{\log a}$ NOT $\frac{a^x}{\log a}$ (false)
(B) $\frac{d}{d x} e^{ax}=a e^{ax}$ (true)
(C) $\frac{d}{d x} x^x = x^{x(1+\log x)}$ and NOT $x.x^{x-1}$ false
(D) $\frac{d}{d x} x^{a}=a x^{a-1}$ (true)
(E) $\frac{d}{d x} a^{a}=0$ (true)