Find the maximum value of the function `f(x) =sin x + cos x`.

Explanation

To find the maximum value of the function \( f(x) = \sin x + \cos x \), we will use the method of derivatives. Here are the steps to solve the problem:

### Step 1: Find the first derivative
We start by differentiating the function \( f(x) \):
\[ f'(x) = \frac{d}{dx}(\sin x + \cos x) = \cos x - \sin x \]

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