If f(x) = 10 cos x + (13 + 2x) sin x, then f' | vedclass

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(A) Given $f(x) = 10 \cos x + (13 + 2x) \sin x$. First, find the first derivative $f'(x)$ using the product rule: $f'(x) = -10 \sin x + [2 \sin x + (1

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$4 \cos x$

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(A) Given $f(x) = 10 \cos x + (13 + 2x) \sin x$. First, find the first derivative $f'(x)$ using the product rule: $f'(x) = -10 \sin x + [2 \sin x + (13 + 2x) \cos x] = -8 \sin x + (13 + 2x) \cos x$. Now, find the second derivative $f''(x)$: $f''(x) = -8 \cos x + [2 \cos x - (13 + 2x) \sin x] = -6 \cos x - (13 + 2x) \sin x$. Finally, calculate $f''(x) + f(x)$: $f''(x) + f(x) = [-6 \cos x - (13 + 2x) \sin x] + [10 \cos x + (13 + 2x) \sin x] = 4 \cos x$.

If $f(x) = 10 \cos x + (13 + 2x) \sin x$, then $f''(x) + f(x)$ is equal to

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