$f (x) = 10 cos x + (13 + 2 x) sin x$ then $f^{^{''}} (x) + f (x) =$

c o s x

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4 c o s x

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s i n x

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4 s i n x

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Solution

The correct option is C $4 c o s x$
Given, $f (x) = 10 cos x + (13 + 2 x) sin x$
$f^{'} (x) = - 10 sin x + (13 + 2 x) cos x + sin x (2)$
$f^{''} (x) = - 10 cos x + (13 + 2 x) (- sin x) + cos x (2) 2 cos x$
$= - 10 cos x - (13 + 2 x) (sin x) + 4 cos x$
$∴ f^{''} (x) + f (x) = 4 cos x$

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