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Find the second derivative of \(y=\sin x+\cos x\) 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

Differentiating once gives \(y'=\cos x-\sin x\). Differentiating again gives \(y''=-\sin x-\cos x=-(\sin x+\cos x)\).

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