Q. $\frac{d}{dx}\ \left\lbrack x^{x} + x^{a} + a^{x} + a^{a} \right\rbrack = \ldots,a$ is constant
A) $x^{x}(1 + \log{x) + a.x^{a - 1}}$
B) $x^{x}(1 + \log{x) + a}.x^{a - 1} + a^{x}\log a$
C) $x^{x}(1 + \log{x) + a^{a}\ \ (1 + \log{a)}}$
D) $x^{x}\left( 1 + \log x \right) + a^{a}(1 + \log a) + ax^{a - 1}{+ a}^{a}(1 + \log{a)}$
Explanation
(b)
$\ \frac{d}{dx}\lbrack x^{x} + x^{a} + a^{x} + a^{a}\rbrack$
$= x^{x}(1 + \log{x) + ax^{a - 1} + a^{x}\log{a + 0}}$
$= x^{x}(1 + \log{x) + ax^{a - 1} + a^{x}\log a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.