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If y = sin(x) + cos(x), find d²y/dx².

1. sin(x) + cos(x)
2. -sin(x) + cos(x)
3. -(sin(x) + cos(x))
4. None of these

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

Solution

Differentiating sin(x)+cos(x) once gives cos(x)-sin(x), and differentiating again gives -sin(x)-cos(x) = -(sin(x)+cos(x)).

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