Q. If $f(x) = 10\cos{x + (13 + 2x)\sin{x,\ \ \ then\ f^{''}(x) + f(x)}\ }$is equal to
A) $\cos x$
B) $4\cos x$
C) $\sin x$
D) $4\sin x$
Explanation
(b)
Given,
$f(x) = 10\cos{x + (13 + 2x)\sin x}$
$\Rightarrow \$ $f^{'}(x) = - 10\sin{x + (13 + 2x)\cos{x + 2\sin x}}$
$\Rightarrow {\ f}^{''}(x) = - 10\cos{x - (13 + 2x)\sin{x + 2\cos{x + 2\cos x}}}\$
$\Rightarrow \ f^{''}(x) = - f(x) + 4\cos x$
$\therefore\ f^{''}(x) + f(x) = 4\cos x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.