Q. $f(x) = e^{x}\sin x,\ then\ f^{''}(x)$ is equal to
A) $e^{6x}\sin{6x}$
B) $2e^{x}\cos x$
C) $8e^{x}\sin x$
D) $8e^{x}\cos x$
Explanation
(b)
Given, $f(x) = e^{x}\sin x$
$\Rightarrow \ \ \ f^{'}(x) = e^{x}\cos{x + \sin{xe^{x}}}$
$\Rightarrow \ \ \ f^{''}(x) = \ e^{x}\cos{x - e^{x}\sin x + e^{x}\sin{x + e^{x}\cos{x\ }}}$
$= \ 2e^{x}\cos x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.