Question

$f\left(x\right)=10\cos x+(13+2x)\sin x$ then $f^{{}^{\prime \prime }}\left(x\right)+f\left(x\right)=$

• A. $cosx$
• B. $4cosx$
• C. $sinx$
• D. $4sinx$

Answer 1

Answer: (B)

$4cosx$

Given, $f\left(x\right)=10\cos x+(13+2x)\sin x$
$f^{\prime }\left(x\right)=-10\sin x+(13+2x)\cos x+\sin x\left(2\right)$
$f^{\prime \prime }\left(x\right)=-10\cos x+(13+2x)(-\sin x)+\cos x\left(2\right)2\cos x$
$=-10\cos x-(13+2x)\left(\sin x\right)+4\cos x$
$\therefore f^{\prime \prime }\left(x\right)+f\left(x\right)=4\cos x$