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Find the second derivative of the function \(y=\sin x+\cos x\) with respect to \(x\).

1. \(-\sin x-\cos x\)
2. \(-\sin x+\cos x\)
3. \(\sin x+\cos x\)
4. \(-\tan x-\cos x\)

Correct answer: \(-\sin x-\cos x\)

Solution

For \(y=\sin x+\cos x\), the first derivative is \(y'=\cos x-\sin x\). Differentiating again gives \(y''=-\sin x-\cos x\).

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