Q. If $f:R \rightarrow R$ is an even function having derivatives of all orders, then an odd function among the following is
A) $f^{''}$
B) $f^{'''}$
C) $f^{'} + f^{''}$
D) $f^{''} + f^{'''}$
Explanation
(b)
Let $f(x) = \cos{x,\ f^{'}(x) = \sin x}$
$\Rightarrow \ {\ f}^{''}(x) = \ - \cos x$
$\Rightarrow \ f^{'''}(x) = \sin x$
Since, $\sin{x\ }$is an odd function.
$\therefore\ \ f^{'''}$ is an odd function.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.